Question

At 10 AM on April 26, 2009, a building 300 feet high casts a shadow 50 feet long. What was the angle of elevation of the Sun?

Short answer

The angle of elevation of the Sun is$80.5376°.$

Step-by-step solution

Given Information

Given that at 10 AM on April 26, 2009, a building 300 feet high casts a shadow 50 feet long.

Solution

Suppose the angle of elevation of the Sun is $x°.$

We can draw a figure of given problem as:

Now, in $△ABC$we have to find angle $B=x°$.

So,

$$\begin{gathered} \tan (x°)=\frac{AC}{BC} \\ \tan (x°)=\frac{300}{50} \\ \tan (x°)=6 \\ x°={\tan }^{-1}\left(6\right) \\ x°=80.5376° \end{gathered}$$

So, the angle of elevation of the Sun is$80.5376°.$