Question

a blimp, suspended in the air at a height of 600 feet, lies directly over a line from a sports stadium to a planetarium. if the angle of depression from the blimp to the stadium is 33° and from the blimp to the planetarium is 28°, find the distance between the sports stadium and the planetarium. the distance between the sports stadium and the planetarium is 2052.52 feet. (round to two decimal places as needed.)

Explanation:

Step1: Find horizontal distance to stadium

Let \( x \) be the horizontal distance from blimp to stadium. Using \(\tan(33^\circ)=\frac{600}{x}\), so \( x = \frac{600}{\tan(33^\circ)} \). Calculate \(\tan(33^\circ)\approx0.6494\), then \( x \approx \frac{600}{0.6494}\approx923.93 \) ft.

Step2: Find horizontal distance to planetarium

Let \( y \) be the horizontal distance from blimp to planetarium. Using \(\tan(28^\circ)=\frac{600}{y}\), so \( y = \frac{600}{\tan(28^\circ)} \). Calculate \(\tan(28^\circ)\approx0.5317\), then \( y \approx \frac{600}{0.5317}\approx1128.59 \) ft.

Step3: Total distance between stadium and planetarium

Add \( x \) and \( y \): \( 923.93 + 1128.59 = 2052.52 \) ft.

Answer:

2052.52 feet