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, the shadow is the adjacent side, and the angle of elevation \(\theta\) is the angle we want to find), 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, \(\tan^{-1}(0.925)\approx43.0^{\circ}\) (rounded to the nearest degree).

Answer:

\(43\)