Question

A blimp is 1100 meters high in the air and measures the angles of depression to two stadiums to the west of the blimp. If those measurements are 75.2° and 17.9°, how far apart are the two stadiums?

Answer 1

Answer:

The two stadiums are approximately 3115.1 meters away from each other

Step-by-step explanation:

Since we can construct two right angle triangles between the blimp and the two stadiums as shown in the attached image, then the distance "x" between the two can be find as the difference between the right triangle legs that extend on the ground.

In order to find the size of such legs, one can use the tangent function of the given depression angles as shown below:

$tan(75.2^o)=\frac{1100}{a} \\a=\frac{1100}{tan(75.2^o)}\\a\approx 290.6\,\,meters$

and for the other one:

$tan(17.9^o)=\frac{1100}{b} \\b=\frac{1100}{tan(17.9^o)}\\b\approx 3405.7\,\,meters$

The the distance between the stadiums is the difference:

b - a = 3405.7  - 290.6 meters = 3115.1  meters