Question

A hot-air balloon is floating above a straight road. To estimate their height above the ground, the balloonists simultaneously measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon. The angles of depression are found to be 18° and 20°. How high is the balloon? (Round your answer to one decimal place.)

Answer 1

Answer:

3.1 miles

Explanation:

To solve this question it is important to remember that the distance between two mile markers is approximately 1 mile

Once this is known, the question becomes very easy to solve. We make two triangle, which have the following three points

Triangle 1: Hot-Air-Balloon, Ground, Milepost 1 - With angle of depression 20

Triangle 2: Hot-Air-Balloon, Ground, Milepost 2 - With angle of depression 18

As a reminder, the angle of depression is simply the angle the balloonist's head makes with the horizontal plane to be able to see the milepost.

From this we can simply drive two formulas using the Tan function

Equation 1 - $Tan(90-18) = \frac{b+1}{h}$

Equation 2 - $Tan(90-20) = \frac{b}{h}$

Solving them simultaneously we get the value of height (h) to be 3.0852 miles or 3.1 miles