Question

Find the shadow cast by a 10 foot lamp post when the angle of elevation of the sun is 58°. Find the length to the nearest tenth of a foot. ... 16.0 ft 6.2 1 209

Answer 1

Given the information on the problem, we can draw the following right triangle:

using the tangent function, we have the following:

$\begin{gathered} \tan (58)=\frac{\text{opposite side}}{adjacent\text{ side}}=\frac{10}{s} \\ \Rightarrow\tan (58)=\frac{10}{s} \end{gathered}$

solving for 's', we get:

$\begin{gathered} \tan (58)=\frac{10}{s} \\ \Rightarrow s\cdot\tan (58)=10 \\ \Rightarrow s=\frac{10}{\tan (58)}=6.2 \end{gathered}$

therefore, the length of the shadow is 6.2 ft