SOLUTION: Observers P and Q are located on the side of a hill inclined at 32°to the horizontal. The observer at P determines the angle of elevation to a hot-air balloon to be 52°. At the s
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Question 1154847: Observers P and Q are located on the side of a hill inclined at 32°to the horizontal. The observer at P determines the angle of elevation to a hot-air balloon to be 52°. At the same time, the observer at Q measures the angle of elevation to the balloon to be 61°. If P is 60m down the hill from Q, find the distance from Q to the balloon. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Observers P and Q are located on the side of a hill inclined at 32°to the horizontal.
The observer at P determines the angle of elevation to a hot-air balloon to be 52°.
At the same time, the observer at Q measures the angle of elevation to the balloon to be 61°.
If P is 60m down the hill from Q, find the distance from Q to the balloon.
:
Since they just want the dist from Q to the balloon, the fact that it is on a hill can be ignored. (assume the angles are measured from the surface they are on, not to the horizontal).
Solve a triangle that is formed by P, Q, and B (balloon)
P = 52 degrees,
the interior angle at Q: 180 - 61 = 119 degrees
Angle B = 180 - 52 - 119 = 9 degrees
Using the law of sines, (p = the dist from Q to B) =
cross multiply
sin(9)*p = 60 * sin(52)
.1564p = 47.2806
p =
p = 302.3 meters from Q to the balloon
