Question

a tower that is 111 feet tall casts a shadow 120 feet long. find the angle of elevation of the sun to the nearest degree.
the angle of elevation is degrees. (round to the nearest degree.)

Explanation:

Step1: Use the tangent function

In a right - triangle (where the tower is the opposite side and the shadow is the adjacent side with respect to the angle of elevation \(\theta\)), the tangent function is defined as \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, the opposite side \(a = 111\) and the adjacent side \(b=120\), so \(\tan\theta=\frac{111}{120}\).

Step2: Simplify the fraction

\(\frac{111}{120}=\frac{37}{40}=0.925\).

Step3: Find the angle using the inverse tangent function

We know that \(\theta=\tan^{- 1}(0.925)\). Using a calculator, \(\tan^{-1}(0.925)\approx43\) (rounded to the nearest degree).

Answer:

\(43\)