Question

3. A building that is 75 feet tall casts a shadow that is 61 feet long. What is the angle of elevation that the sun makes with the ground?

Answer 1

`\begin{gathered} we\text{ know that for an angle }\alpha,\text{ } \\ \tan (\alpha)=\frac{\text{opposite side of angle}}{\text{ adjacent side of angle}} \\ \tan (\alpha)=(75)/(61) \\ \text{ Applying tan}^(-1)\text{ to both sides of the equation yields} \\ \\ \tan ^(-1)(\tan (\alpha))=\tan ^(-1)((75)/(61)) \\ \alpha=\tan ^(-1)((75)/(61)) \\ \alpha=50.88\degree \\ \text{the elevation angle is 50.88\degree} \end{gathered}`