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 22° and 24°. How high is the balloon?

Answer 1

Answer:

3.56 mi

Explanation:

from the question we are given the following:

first angle of depression = 22 degrees

second angle of depression = 24 degrees

find the height of the hot air baloon

First we have to take note of the following

• That the distance between two successive mileposts is 1 mile
• The angle of elevation from the mileposts will be 22 degrees and 24 degrees because they are alternate angles with the angles of depression
• I attached a diagram to to illustrate the above points

for the smaller triangle tan 24 = \frac{h}{p}

h = p × tan 24 ... equation 1

for the bigger triangle tan 22 = \frac{h}{p +1}

h = {p +1} x tan 22  ..... equation 2

now equating the two equations for h we have

p x tan 24 = {p+1} x tan 22

0.45 p = 0.4 {p+1}

1.125 p = p + 1

1.125 p - p = 1

p = \frac{1}{0.125} = 8

now we can substitute the value of p into equation 1

h = p x tan 24

h = 8 x tan 24 = 3.56 mi