Question

question 13 (multiple choice worth 4 points)
(08.03 mc)
ema is standing in a trechouse and looking down at a swingset in the yard next door. the angle of depression from emirs eyeline to the swingset is 33.69°, and emir is 10 feet from the ground. how many feet is the base of the tree from the swingset? round your answer to the nearest foot.
o 15 feet
o 18 feet
o 20 feet
o 24 feet

Explanation:

Step1: Use the tangent function

The angle of depression is \(33.69^{\circ}\), and Emir's height from the ground is \(10\) feet. Let \(x\) be the horizontal distance (base of the triangle). The tangent of an angle in a right - triangle is given by \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 33.69^{\circ}\) and the opposite side (Emir's height) \(y = 10\) feet. So, \(\tan(33.69^{\circ})=\frac{10}{x}\).

Step2: Solve for \(x\)

We know that \(x=\frac{10}{\tan(33.69^{\circ})}\). Using a calculator, \(\tan(33.69^{\circ})\approx0.666\). Then \(x=\frac{10}{0.666}\approx15\)

Answer:

\(15\) feet