If the hypotenuse of a 30°-60°-90° Triangle is 10√2, find the length of the other two sides.

Answers

Answer 1

Let us consider a 30°-60°-90°△ABC right angled at B in which ∠C = 30⁰ and ∠A = 60⁰ with hypotenuse AC = 10√2 units.

Solution:-

In △ABC,

[tex]\longrightarrow[/tex]sin ∠C = [tex]\sf \dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]\longrightarrow[/tex]sin ∠C = [tex]\sf \dfrac{AB}{AC}[/tex]

[tex]\longrightarrow[/tex]sin 30⁰ = [tex]\sf \dfrac{AB}{10\sqrt{2}}[/tex]

[tex]\longrightarrow[/tex][tex]\sf \dfrac{1}{2}= \dfrac{AB}{10\sqrt{2}}[/tex]

[tex]\longrightarrow[/tex][tex]\sf AB = \dfrac{10\sqrt{2}}{2}[/tex]

[tex]\longrightarrow[/tex][tex]\sf AB = 5\sqrt{2}\:units[/tex]

[tex]\\[/tex]

In △ABC,

[tex]\longrightarrow[/tex]cos ∠C = [tex]\sf \dfrac{Base}{Hypotenuse}[/tex]

[tex]\longrightarrow[/tex]cos ∠C = [tex]\sf \dfrac{BC}{AC}[/tex]

[tex]\longrightarrow[/tex]cos 30⁰ = [tex]\sf \dfrac{BC}{10\sqrt{2}}[/tex]

[tex]\longrightarrow[/tex][tex]\sf \dfrac{\sqrt{3}}{2}= \dfrac{BC}{10\sqrt{2}}[/tex]

[tex]\longrightarrow[/tex][tex]\sf BC = \dfrac{10\sqrt{2}\times \sqrt{3}}{2}[/tex]

[tex]\longrightarrow[/tex][tex]\sf BC = \dfrac{10\sqrt{2\times 3}}{2}[/tex]

[tex]\longrightarrow[/tex][tex]\sf BC = \dfrac{10\sqrt{6}}{2}[/tex]

[tex]\longrightarrow[/tex][tex]\sf BC = 5\sqrt{6}\: units[/tex]

Thus , the length of other two sides of triangles are 5√2 and 5√6 units.

If The Hypotenuse Of A 30-60-90 Triangle Is 102, Find The Length Of The Other Two Sides.

Related Questions

Subway creates a paid promotion featuring a different 6-inch sub of the day each day of the week. The sub of the day is only $3. 50. Subway utilizes the radio to spread the word. Which promotion method is subway using?.

Answers

Based on the information provided, the promotion method subway is using is sales promotion.

What is promotion?

It is a marketing tool that involves letting know potential customers about a product that a company wants to sell.

What are the promotion methods?

Most common methods include:

Direct selling.Public relations.Sales promotion.

What is sales promotion?

This involves promoting or advertising products through sales, which means customers are offered special discounts or lower prices. This is the method used by the subway because the sub of the day is a sales.

Learn more about sales in: https://brainly.com/question/15375944

A triangle has two sides of length 19 and 15. What is the largest possible whole-number length for the third side?

Answers

Answer:

34? Idek

Step-by-step explanation:

Answer:

33

Step-by-step explanation:

To maximize the length of the third side, which I'll call x, it needs to be the longest side.

So by the triangle inequality theorem, 19+15>x, meaning the maximum whole number value of x is 33.

Find the area. What type of triangle is triangle ABC?

Answers

Answer:

Isosceles right triangles are half squares, and if the length of one side is 6cm, that is the length of the other side since both segments are equal. Take the formula to find the area of a square (base times height), apply the side measurement of the triangle (6cm) and divide it in half to find the area of half of it (therefore, finding the area of the isosceles triangle.) (6x6) / 26x6 = 3636 / 2 = 18 The area of the isosceles triangle is 18 square centimeters.

Step-by-step explanation:

Elaine sold twice as many T-shirts as Kim
How many did each girl sell if the total
number of T-shirts sold was 27?
(no links no files) I need equation

Answers

x + 2x = y this equation will solve the problem

help pls first correct answer gets brainleist ​

Answers

n²= 7²+3²

=49+9

=58

n= V58

=7.62m

Whoever answers first gets 30 points plus brainliest

how many months are there in 7 years???

good luck ;)

Answers

Answer:

84

Step-by-step explanation:

1 year= 12 months

7 years × 12 months each= 84 months in total for 4 years

Can someone help me out with this?

What is the value of x?



Enter your answer in the box.

Answers

Answer:

x = 4

Step-by-step explanation:

x has the same value as RT since they are equal sides of the isosceles triangle.

RT is also the hypotenuse of ΔRST - 30°×60°×90° right triangle.

Acoording to the property of such triangles, the ratio of sides is:

a : b : c = 1 : √3 : 2

We have:

b = 2√3 and c = RT

Use the ratio to find the lenght of RT

2√3 : RT = √3 : 2RT = 2*2√3/√3RT = 4

So the value of x is 4 units

Find RT

sin60=2√3/RT√3/2=2√3/RTRT=4√3/√3RT=4

Now

tan45=x/4x=4

Use the ordered pairs below. (10,20), (11, 21), (12, 22) What patterns are used to create the ordered pairs?​

Answers

Answer:

Add 1 unit to the X coordinates and Y coordinates for each new pair.

step-by-step explanation:

X: 10 + 1 = 11 + 1 = 12

Y: 20 + 1 = 21 + 1 = 22

The normal price of a television is £1200
It is reduced to £970
Work out the percentage reduction.
Give your answer to 1 decimal place

Answers

Answer:80.8%

Step-by-step explanation:

£1200=100%

£970=

£970*100%/£1200=80.8333333

80.8%

Answer:

19.2%.

Step-by-step explanation:

Reduction = 1200-970 = £230,

% reduction = 230*100/ 1200

= 19,2%

2/5 g+3h -6 when g=10 h=6

Answers

hello!

let's evaluate this expression

[tex]\pmb{\displaystyle\frac{2}{5}g+3h-6 }[/tex]

[tex]\pmb{\displaystyle\frac{2}{5} *10+3(6)-6}[/tex]

[tex]\pmb{\displaystyle\frac{2}{5} *10+18-6}[/tex]

[tex]\pmb{\displaystyle\frac{2}{5} *10+12}[/tex]

Multiply:

[tex]\pmb{\displaystyle\frac{2}{5} *\frac{10}{1} =\frac{20}{5} =4}[/tex]

Final Step:-

[tex]\pmb{4+12}[/tex]

[tex]\pmb{16}[/tex]

======================================================

note:-

Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I'll comment and/or edit my answer :)

Angle 1 and Angle _____________ are supplementary angles.

Answers

Answer: number 2

Step-by-step explanation: so a supplementary Angle adds up to a 180 angle so it would be number 2 I think.

how do you do thissss???

Answers

The solid above is a triangular prism. Therefore, the surface area of the triangular prism is 157.2 cm².

How to calculate surface area

The figure above is a triangular prism. The surface area of a triangular prism can be calculated as follows:

Surface area = bh + l(p)

where

p = perimeter of the triangular basel = height of prismb = base of the triangular baseh = height of the triangular base

Therefore,

p = 6 + 6 + 6 = 18 cm

l = 7 cm

b = 6 cm

h = 5.2 cm

Therefore,

Surface area = (6 × 5.2) + 7(18)

Surface area = 31.2 + 126

Surface area = 157.2 cm²

learn more on surface area here: https://brainly.com/question/2835293

What is the value of k?​

Answers

Answer:

10°

Step-by-step explanation:

According remote interior angles, 4k + 5 + 6k + 10 = 115.

10k + 15 = 115

10k = 100

k = 10

Hope this helps :)

Have a nice day!

Answer:

k = 10°

Step-by-step explanation:

      According to the exterior angle theorem, the exterior angle will be equal to the two opposite inside angles added together. It will look like the following, and we solve for k from there.

115° = (4k + 5)° + (6k + 10)°

115° = 4k° + 5° + 6k° + 10°

115° = 6k° + 4k° + 10°  + 5°

115° = 10k° + 15°

100° = 10k°

10° = k

k = 10°

Natoshia's den is 4 feet longer than it is wide. If the​ den's area is 320 square​ feet, what are the dimensions of the​ room?

Answers

Dimensions : 16 x 20

Let the width be xthen the length: x + 4

                     area of rectangle = Length * Width

solving steps:

(x+4)(x) = 320x² + 4x = 320x² + 4x - 320 = 0x² +20x -16x -320 = 0x(x + 20) -16(x+20) = 0(x-16)(x+20) = 0x = 16, -20x = 16                     [ As length or width can never be negative ]

So we found Width = 16 feet

Length:

16 + 420 feet

Answer:

width = 16 ft

length = 20 ft

Step-by-step explanation:

Let width = x

If the length is 4 ft longer than the width, then

⇒ length = x + 4

Area of a rectangle = width × length

Given:

area = 320width = xlength = x + 4

Substituting these values into the equation for the area of a rectangle and solving for x:

⇒ 320 = x(x + 4)

⇒ 320 = x² + 4x

⇒ x² + 4x - 320 = 0

⇒ (x - 16)(x + 20) = 0

⇒ x = 16, -20

As distance is positive, then x = 16 only.

Therefore, width = 16 ft and length = 20 ft

An aluminum bar 3 feet long weighs 12 pounds. What is the weight of a similar bar that is 3 feet 4 inches long?

Answers

Answer: 13 [tex]\frac{1}{3}[/tex] pounds

Step-by-step explanation:

     We will set up a proportion. I will have the weight, in pounds, on the top (numerator) and the length, in inches, on the bottom (denominator).

[tex]\frac{12}{36} =\frac{x}{40}[/tex]

     Cross-multiply:

36 * x = 12 * 40

36x = 480

     Divide both sides of the equation by 36:

x = 13 [tex]\frac{1}{3}[/tex] pounds

Answer:

Step-by-step explanation:

First find unit weight.

1 foot = 12 inches

3 ft = 3*12 = 36 inches

3ft 4 inches = 36 + 4 = 40inches

Weight of 36 inches  long bar =   12  pounds

Weight of 1 inch bar = 12/36

[tex]\text{Weight of 40 inches long bar = $\dfrac{12}{36}*40$}[/tex]

                                             = 13.3 pounds

                                                     

If and , which expression is equivalent to ?

A.

B.

C.

D.

Answers

do you have an image or more text for this because it doesn’t make sense as it is

Consider the quadratic function.
f(x)=x^(2)+2x-15
If the line of symmetry of the function is located at x=N, what is the value of N?
HELP ASAP

Answers

Answer:

N = -1

explanation:

x = N

solving steps:

[tex]\sf f(x)=x^2+2x-15[/tex]

To find symmetry of a quadratic function.

                                                                   vertex formula    :   [tex]\sf x=\dfrac{-b}{2a}[/tex]

[tex]a=1,\:b=2[/tex]

[tex]\sf x=\dfrac{-2}{2\cdot \:1}[/tex]

[tex]\sf x = -1[/tex]

Then,

N = -1

Pllllssss answer!! i only have a few more minutess!! (i'll give brainilest) tyler wants to buy some cherries at the farmer's market. he has $ 10 and cherries cost $4 per pound. 1. if c is the number of pounds of cherries that tyler can buy, write one or more inequalities or equations describing c. 2. can 2 be a value of c? can 3 be a value of c? what about -1? explain your reasoning. 3. if m is the amount of money, in dollars. tyler can spend, write one or more inequalities or equations describing m. 4. can 8 be a value of m? can 2 be a value of m? what about 10.5? explain your reasoning. did you answer all 4 parts?​

Answers

answer:

step by step explanation:

10-4 = c

6 = c

he can buy 2 pounds of cherries

2. 2 can be the value of c

c = 2

10- 4c

10- 4(2)

10 - 8 = 2

c = 3

10 - 4c

10- 4(3)

10 - 12 = -2

c = -1

10 - 4(-1)

10 - (-4)

10 + 4

= 14

manage this

mark me brainliest

Please Help this is due soon

The table below represents an exponential function.

table represents an exponential function.
What is the interval between neighboring
x-values shown in the table?
1
What is the ratio between neighboring y-values?
4
What is the equation for this pattern?
y = _^x

I only need the last one answered

Answers

Answer:

[tex]y = {4}^{x} [/tex]

is the answer

Trigonometry, how would I find the area of this triangle?

Answers

Answer:

Step-by-step explanation:

Area of triangle = 1/2 * base * height

Use the side of length 5.6cm as base, the height will be a perpendicular line from the base to the tip of the triangle.

From the right-angle triangle formed by the height and the side of length 3.9cm,

sin(56°45') = height / 3.9

height = 3.9*sin(56°45')

Substituting back into the area equation:

Area = 1/2*5.6*3.9*sin(56°45')

= 9.0cm^2

= 9cm^2

Use sine rule for Area

[tex]\\ \rm\rightarrowtail Area=\dfrac{1}{2}absinC[/tex]

[tex]\\ \rm\rightarrowtail Area=\dfrac{1}{2}(3.9)(5.6)sin56°45'[/tex]

[tex]\\ \rm\rightarrowtail Area=10.92(0.836)[/tex]

[tex]\\ \rm\rightarrowtail Area=10.22cm^2[/tex]

Solve the system of equations at right. 2^(x+y)=16 2^(2x+y)= 1/8

Answers

Answer:

  (x, y) = (-7, 11)

Step-by-step explanation:

The system of exponential equations can be solved by the use of logarithms. Equivalently, the equations can be written so that exponents can be equated. This system is equivalent to two linear equations.

First equation:

  2^(x+y) = 16

  2^(x +y) = 2^4 . . . . use the same base to write the constant

  x +y = 4 . . . . . . . . equate exponents of 2 (take log₂ of both sides)

Second equation:

  2^(2x +y) = 1/8

  2^(2x +y) = 2^(-3) . . . . use the same base to write the constant

  2x +y = -3 . . . . . . equate exponents of 2

Solve the linear equations:

We can subtract the first equation from the second to get ...

  (2x +y) -(x +y) = (-3) -(4)

  x = -7

  y = 4 -x = 4 -(-7) = 4 +7 = 11 . . . . use the first equation to find y

The solution to the system is (x, y) = (-7, 11).

is 48,200 in scientific notation?

Answers

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \:48200[/tex]

[tex]\qquad \sf  \dashrightarrow \:4.82 \times 10 {}^{4} [/tex]

There are exactly 4 parts to this question so if u can please answer thanks

Part A
Dilate Triangle OPQ with a scale factor of 1/2.
Provide the coordinates of each new vertex.

Part B
How does the size Triangle O'P'Q' compare to the size of Triangle OPQ?
Explain how this relates to the scale factor.

Part C
Are
Part D
If the length of segment OQ measures 9.8 units, what is the length of segment O'Q'? Explain in terms of similarity.

Answers

Answer:

see my question and come there now I want to talk with you

Step-by-step explanation:

Goal: illustrates radius, diameter, chord, center, arc, central angle, and

inscribed angle.

Role: Garden Designer/Landscape Architect

Audience: Math Teacher

Situation: A certified plantita and backyard owner plans to have a unique

garden. As a Landscape Architect, you are asked to make a sample layout of

a circular garden. She asks you to include the following on her garden:

● well

● pond

● bridge

● fountain

● walkways

● benches or chairs

● entrance and exit gates.

● trees, ornamental plants, and herbs

Procedure:

1. Draw a circle.

2. Conceptualize a circular garden and layout using the specified

items mentioned above.

What I Can Do

9

DISCIPLINE • GOOD TASTE • EXCELLENCE

3. Label the parts of circle formed on the garden layout

Please I'm looking for a serious answer. I need to pass this on monday. Thank you.

Y^2+8y+2 y=-5 evaluate the expression

Answers

Answer:

the correct answer is shown below

Step-by-step explanation:

hope this helps

have an awesome day -TJ

pls mark brainliest if this helps :)

An object is attached by a string to the end of a spring. Fang throws the object upwards and starts a stopwatch at t=0t=0t, equals, 0 seconds. The object starts oscillating vertically in a periodic way that can be modeled by a trigonometric function.
The object's average height is -20\text{ cm}−20 cmminus, 20, start text, space, c, m, end text (measured from the top of the spring). It first achieves that average height on the way up at t=0.2t=0.2t, equals, 0, point, 2 seconds, and then again every 222 seconds. The object's maximum and minimum heights are each 5\text{ cm}5 cm5, start text, space, c, m, end text from its average height.
Find the formula of the trigonometric function that models the height HHH of the weight ttt seconds after Fang started the stopwatch. Define the function using radians.
\qquad H(t) =H(t)=H, left parenthesis, t, right parenthesis, equals
What is the height of the object after 0.60.60, point, 6 seconds? Round your answer, if necessary, to two decimal places.

Answers

The object attached to a string illustrates a sinusoidal trigonometric function

The trigonometric function is H(t) = 5sin(π/2(t-0.2))-20, and the object's height after 0.6 seconds is  -17.06 cm

How to determine the trigonometry function model?

The trigonometry model of the object is a sine function represented by:

H(t) = Asin(B(t - c)) + D

The maximum height is 5 cm.

So, we have:

Amplitude, A = 5

The average height is - 20 cm.

So, we have

Vertical shift, D = -20

Its first average height is at t = 0.2.

So, we have:

Horizontal shift, C = 0.2

The period B is then calculated as:

B = π/t

The object reaches the maximum height every 2 seconds.

So, we have:

B = π/2

Substitute these values in H(t) = Asin(B(t - c)) + D

H(t) = 5sin(π/2(t-0.2))-20

Hence, the trigonometric function is H(t) = 5sin(π/2(t-0.2))-20

The height of the object after 0.6 seconds

Substitute 0.6 for t in H(t)

H(0.6) = 5sin(π/2(0.6-0.2))-20

Evaluate

H(0.6) = -17.06

Hence, the object's height after 0.6 seconds is  -17.06 cm

Read more about trigonometric functions at:

https://brainly.com/question/10700288

Answer:

What is the importance of biology laboratory?

Biological Science Laboratory Apparatus is essential for meeting our basic needs of food, clothing, shelter, health, energy, clean air, water and soil. Biological Science Laboratory Apparatus enrich the quality of life in numerous ways by providing new solutions to problems in health and materials and energy usage.

Use the definition of continuity and the properties of limits to show that the function k(x)= √8−x2 2x2−5 is continuous at x = -2

Answers

Voy a buscar el número y le digo el resultado

ASAPPPP!! Please!
The histogram shows the number of days in the past week that 30 surveyed people exercised.

Number of Days per person.
And days

How many people who were surveyed exercised fewer than 4 days last week?

12
14
16
18

Answers

Answer:

16

Step-by-step explanation:

2 from 3 days

another 2 on 2 days

5 for 1 day

7 for 0 days

2+2+5+7= 16

Point c is the center of dilation. line segment b a is dilated to create line segment b prime a prime. the length of c a is 4. the length of a a prime is 16. what is the scale factor of the dilation of line segment ba? one-fifth one-fourth 4 5

Answers

The scale factor of the dilation of line segment ba for which the center of dilation is C, is 5.

What is the dilation of the figure?

Dilation of a figure, means the transformation of the figure. The factor by which the given figure dilated, called the scale factor of dilation.

Point c is the center of dilation. Line segment BA is dilated to create line segment b prime, a prime.  The image of the given problem is attached below. The length of CA is 4.

[tex]CA=4[/tex]

The length of a prime is 16.

[tex]AA'=16[/tex]

The new dimension will be,

[tex]CA'=CA+AA'\\CA'=4+16\\CA'=20[/tex]

Now, the scale factor is the ratio of the new dimension to the original dimension. Thus, the scale factor of the dilation is,

[tex]r=\dfrac{20}{4}\\r=5[/tex]

This will be the same for the line segment BA. Thus, the scale factor of the dilation of line segment ba for which the center of dilation is C, is 5.

Learn more about the dilation of the figure here;

https://brainly.com/question/3457976

Answer:

the answer is 5

Step-by-step explanation:

D

1. Janelle began the work below to find 368 ÷ 16. Complete the work.​

Answers

Answer:

23

Step-by-step explanation:

[tex]368/16=23[/tex]

23 is the answer because if you divide the answer will be 23.

How do solve this
h(x)=1/2x-14; h(4)

Answers

Answer:

-12

Step-by-step explanation:

h(x) = ½x - 14 where x = 4:

h(4) = ½(4) - 14

= 2 - 14

= -12

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