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1 year ago

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Louie is trying to find a rectangular canvas for his art project. its width must measure 20 inches and form a 35° angle with the

diagonal of the canvas. what is the height of the canvas? round your answer to the nearest tenth.

1 answer:

sweet-ann [11.9K]1 year ago

8 0

The height of the canvas according to tangent is 14 inches.

According to the statement

we have given that the a rectangular canvas for his art project. its width must measure 20 inches and form a 35° angle with the diagonal of the canvas.

And we have to find the height of the canvas.

So, For this purpose,

The given information is:

The 35⁰ angle is part of a right triangle with a side of 20 inches. The tangent of this angle (35⁰) is equal to the opposite side, x, over the adjacent side (20 inches).

Tan (35⁰) = x/20

0.7002 = x/20

x = 14.004 inches.

For more understanding of the statement please see the image below.

So, The height of the canvas according to tangent is 14 inches.

Learn more about tangent here

brainly.com/question/17040970

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Need help on these trig homework

allochka39001 [22]

8. The length of the support is 7. 9 m

9. The length of the conveyer is 12m

3. a = 59m

A = 44°

B = 52°

4. c = 88. 6 mm

b = 49. 1 m

B = 34°

<h3>How to solve the trigonometry</h3>

8. We have the angle to be 20 degrees

Opposite side = x

hypotenuse = 23m

Using the sine ratio

sin θ = opposite/ hypotenuse

$sin 20 = \frac{x}{23}$

Cross multiply

$sin 20$ × $23 = x$

$x = 0. 3420$ × $23$

x = 7. 9 m

The length of the support is 7. 9 m

9. The angle of elevation is 37. 3 degrees

Hypotenuse = 19 . 0m

Opposite = x

Using the sine ratio

sin θ = opposite/ hypotenuse

$sin 37. 3 = \frac{x}{19}$

cross multiply

$x = 0. 6059$ × $19$

x = 11.5

x = 12 m in 2 significant figures

The length of the conveyer is 12m

3. To determine the sides and angles, we use the sine rule;

$\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}$

For side a, we use the Pythagorean theorem

$c^2 = a^2 + b^2$

$85^2 = a^2 + 67^2$

$a = \sqrt{89^2-67^2}$

$a = \sqrt{3432}$

a = 58. 58, a = 59m

To find angle A and B, use the sine rule

$\frac{59}{sin A } = \frac{85}{sin 90}$

cross multiply

$sin A$ × $85$ = $sin 90$ × $59$

make sin A subject of formula

$sin A = \frac{59}{85}$

$sin A = 0. 6941$

A = $sin^-^1(0. 6941)$

A = 44°

$\frac{67}{sin B} = \frac{85}{sin 90}$

cross multiply

$sin B$ × $85$ = $sin 90$ × $67$

make sin b subject of formula

$sin B = \frac{67}{85}$

$sin B = 0. 7882$

B = $sin^-^1( 0. 7882)$

B = 52°

4. To find the sides, we use the sine rule;

$\frac{74. 0}{sin 56. 6} = \frac{c}{sin 90}$

Cross multiply

$sin 56. 6$ × $c = sin 90$ × $74$

make 'c' subject of formula

$c = \frac{74}{0. 8348}$

c = 88. 6 mm

To find length b, we use the Pythagorean theorem

$c^2 = a^2 + b^2$

$b^2 = c^2 - a^2$

$b^2 = 88. 8^2 - 74^2$

$b = \sqrt{7885. 44 - 5476}\\\\ b = \sqrt{2409. 44}$

b = 49. 1 m

$\frac{74. 0}{sin 56. 6} = \frac{49. 1}{sin B}$

cross multiply

$sin B = \frac{40. 99}{74. 0}$

B = $sin^-^1(0. 5539)$

B = 34°

Learn more about trigonometric identity here:

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1 year ago

What divided by three equals 6

crimeas [40]

Answer:

18

Step-by-step explanation:

18÷3=6

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3 years ago

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Can you help me with this Q i cant get it i have 3 min only please help me :)

Butoxors [25]

x= 3

AC = 22

hope it helps you...

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2 years ago

What is the g.c.f of 18x15

babunello [35]

Answer:

3

Step-by-step explanation:

List all possible factors of each number. The GCF will be the largest number they both share

Factors of 18: 1, 2, 3, 6, 18

Factors of 15: 1, 3, 5, 15

The largest number they both share is 3, so that is the GCF

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3 years ago

How do I solve this problem. I have to find the missing side lengths and lease my sender as radicals in simplest form

nlexa [21]

Answer:

x = y = 2√2

Step-by-step explanation:

Find the diagram attached

To get the unknown side x and y, we need to use the SOH CAH TOA identity

Opposite side = x

Adjacent = y

Hypotenuse = 4

Sin theta = opposite/hypotenuse

sin 45 = x/4

x = 4 sin 45

x = 4 * 1/√2

x = 4 * 1/√2 * √2/√2

x = 4 * √2/√4

x = 4 * √2/2

x = 2√2

Similarly;

cos theta = adjacent/hypotenuse

cos 45 = y/4

y = 4cos45

y = 4 * 1/√2

y = 4 * 1/√2 * √2/√2

y = 4 * √2/√4

y = 4 * √2/2

y = 2√2

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2 years ago