Question

A blimp is 1500 meters high in the air and measures the angles of depression to two stadiums to the west of the blimp. If those measurements are 72.9° and 34.1°, how far apart are the two stadiums to the nearest meter?

Answer 1

The distance between both stadiums is:

2215.49 m - 461.46 m =1754.03 m

Explanation:

Look at the attached picture:

Lets say that the stadium on the left is stadium 1 and stadium 2 is on the right.

Using the angle property of alternate angles the angle above stadium 1 is 72.9° and the angle above the stadium 2 is 34.1°

By using trigonometric function of tangent we solve it as:

We know that tanθ = opposite / adjacent

Therefore,

tan 72.9°=1500/ adjacent

Now

adjacent = 1500/tan 72.9°

adjacent = 461.46 m

Solve for next angle:

Tan 34.1°=1500/ adjacent

adjacent = 1500/tan 34.1°

adjacent = 2215.49 m

Therefore the distance between both stadiums is:

2215.49 m - 461.46 m =1754.03 m ....