Question

question 9
nisha is looking out the window of her apartment building at a sculpture in a park across the street. the top of nishas window is 60 feet from the ground. the angle of depression from the top of nishas window to the bottom of the sculpture is 25°. what is the distance along the ground between the building and the sculpture? round your answer to the nearest hundredth.

Explanation:

Step1: Identify the angle of elevation

The angle of depression from the top of the window to the sculpture is \(25^{\circ}\). The angle of elevation from the sculpture to the top of the window is also \(25^{\circ}\) (alternate - interior angles). The height of the window from the ground is \(h = 60\) feet.

Step2: Use the tangent function

We know that \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 25^{\circ}\) and the opposite side to the angle of elevation is the height of the window (\(h = 60\) feet), and the adjacent side \(x\) is the distance along the ground between the building and the sculpture. So, \(\tan(25^{\circ})=\frac{60}{x}\).

Step3: Solve for \(x\)

We can rewrite the equation as \(x=\frac{60}{\tan(25^{\circ})}\). Since \(\tan(25^{\circ})\approx0.4663\), then \(x=\frac{60}{0.4663}\approx128.67\) feet.

Answer:

128.67 feet