Question

MODELING WITH MATHEMATICS The top of the slide is 12 feet from the ground and has an angle of depression of 53°.What is the length of the slide? Round your answer to the nearest whole number.12 ft53AThe slide is aboutfeet long.

Answer 1

Solution:

From the given figure;

$\begin{gathered} Opposite=12\text{ feet} \\ Hypotenuse=length\text{ of slide} \\ \theta=53\degree \end{gathered}$

Applying SOHCAHTOA

$\begin{gathered} \sin\theta=\frac{Opposite}{Hypotenuse} \\ \sin53\degree=\frac{12}{Hypotenuse} \\ Hypotenuse=\frac{12}{\sin53\degree} \\ Hypotenuse=15.02562=15\text{ feet \lparen nearest whole number\rparen} \end{gathered}$

Hence, the slide is about 15 feet long