Question

a giant, 268 - foot tree casts a smaller, 158 foot shadow. what is the angle of elevation to the sun? 30.52° 38.11° 59.48° 51.89°

Explanation:

Step1: Recall the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, the height of the tree (opposite side) is \(h = 268\) feet and the length of the shadow (adjacent side) is \(x=158\) feet. So, \(\tan\theta=\frac{268}{158}\).

Step2: Calculate the value of \(\tan\theta\)

\(\tan\theta=\frac{268}{158}\approx1.6962\).

Step3: Find the angle \(\theta\)

We know that \(\theta=\tan^{- 1}(1.6962)\). Using a calculator, \(\theta\approx59.48^{\circ}\).

Answer:

\(59.48^{\circ}\)