A ladder, 510 cm long, leans against a building. If the angle between the ground and the ladder is 57 degrees, how far from the wall is the bottom of the ladder? Round to the nearest tenth

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asked Mar 6, 2023 123k views

2 votes

A ladder, 510 cm long, leans against a building. If the angle between the ground and the ladder is 57 degrees, how far from the wall is the bottom of the ladder? Round to the nearest tenth

Mathematics
college

Shahbaz Ahmed asked

by Shahbaz Ahmed

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1 Answer

5 votes

Let's use cosine function to find the distance between the wall and the bottom of the ladder:

$\begin{gathered} \cos (\theta)=(adjacent)/(hypotenuse) \\ \cos (57)=(x)/(510) \\ solve_{\text{ }}for_{\text{ }}x\colon \\ x=510\cdot\cos (57) \\ x=277.8\operatorname{cm} \end{gathered}$