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A ladder 16 feet long leans against the side of a house. Find the height h from the top of the ladder to the ground when the angle of elevation of the ladder is 74°. Round your answer to the nearest tenth.

Respuesta :

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Answer:

15.38 feets

Step-by-step explanation:

Using Pythagoras rule :

Sinθ = opposite / hypotenus

Sin 74 = h / 16

0.9612616 = h / 16

h = 0.9612616 * 16

h = 15.38 feets

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The sine ratio is the ratio of the height of the ladder to length of the

ladder.

Response:

  • The height from the top of the ladder to the ground is h ≈ 15.4 feet

Which method is used to find the height of the ladder?

The length of the ladder = 16 feet

The angle of elevation of the ladder = 74°

Required:

The height of the top of the ladder from the ground, h

Solution:

By trigonometric ratios, we have;

[tex]sin(74^{\circ}) = \mathbf{ \dfrac{h}{16}}[/tex]

Therefore;

h = 16 feet × sin(74°) \approx 15.4 feet

  • The height h from the top of the ladder to the ground is approximately 15.4 feet.

Learn more about sine ratio here:

https://brainly.com/question/16173933

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