Question

If the sun is 62 above the horizon, find the length of the shadow cast by a building 90 ft tall. Round your answer to thenearest tenth.

Answer 1

Answer:

47.9 degrees.

Explanation:

The diagram representing this problem is drawn and attached below:

The length of the shadow cast by the building is labeled x above.

Using trigonometric ratios:

$\begin{gathered} \tan \theta=\frac{\text{Opposite}}{\text{Adjacent}} \\ \implies\tan 62\degree=\frac{90}{x} \end{gathered}$

Next, solve the equation for x:

$\begin{gathered} x\tan 62\degree=90 \\ \text{Divide both sides by }\tan 62\degree \\ \frac{x\tan 62\degree}{\tan 62\degree}=\frac{90}{\tan 62\degree} \\ x=47.85\degree \\ x\approx47.9\degree \end{gathered}$

Thus, the length of the shadow cast by a building 90 ft tall is 47.9 degrees (correct to the nearest tenth).