Question

a blimp, suspended in the air at a height of 400 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 36° 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 feet. (round to two decimal places as needed )

Explanation:

Step1: Find distance from blimp to stadium

Let \( x \) be the horizontal distance from blimp to stadium. Using tangent (opposite/adjacent), \( \tan(36^\circ)=\frac{400}{x} \), so \( x = \frac{400}{\tan(36^\circ)} \).
\( x \approx \frac{400}{0.7265} \approx 550.61 \)

Step2: Find distance from blimp to planetarium

Let \( y \) be the horizontal distance from blimp to planetarium. Using tangent, \( \tan(28^\circ)=\frac{400}{y} \), so \( y = \frac{400}{\tan(28^\circ)} \).
\( y \approx \frac{400}{0.5317} \approx 752.30 \)

Step3: Total distance between stadium and planetarium

Total distance \( = x + y \approx 550.61 + 752.30 = 1302.91 \)

Answer:

1302.91