# Thread: Law of Sines Word Problem

1. ## Law of Sines Word Problem

A man is flying in a hot-air balloon in a straight line at a constant rate of 5 feet per second, while keeping it at a constant altitude. As he approaches the parking lot of a market, he notices that the angle of depression from his balloon to a friend's car in the parking lot is 37°. A minute and a half later, after flying directly over this friend's car, he looks back to see his friend getting into the car and observes the angle of depression to be 31°. At that time, what is the distance between him and his friend?

This is what I did:

(5ft/sec)(90sec)= 450ft

sin112/450 = sin37/x
x=292

sin90/292 = sin59/y
y=250ft <-----not the correct answer to the problem.

any help would be appreciated

2. Originally Posted by maryanna91
A man is flying in a hot-air balloon in a straight line at a constant rate of 5 feet per second, while keeping it at a constant altitude. As he approaches the parking lot of a market, he notices that the angle of depression from his balloon to a friend's car in the parking lot is 37°. A minute and a half later, after flying directly over this friend's car, he looks back to see his friend getting into the car and observes the angle of depression to be 31°. At that time, what is the distance between him and his friend?

This is what I did:

(5ft/sec)(90sec)= 450ft

sin112/450 = sin37/x
x=292

sin90/292 = sin59/y
y=250ft <-----not the correct answer to the problem.

any help would be appreciated
$d = \frac{450\sin(37)}{\sin(112)} = 292$

3. oh wow...i was looking for the wrong distance! thanks for your help!