Question 1034851: Caleb and Emily are standing 100 yards from each other. Caleb looks up at a 45° angle to see a hot air balloon. Emily looks up at a 60° angle to see the same hot air balloon. Approximately how far is the hot air balloon off the ground?
Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website! You'll have to draw the diagram as it is not something I can do here...
Anyway, you'l have two triangles, a 45-45-90 and a 30-60-90...we can use the law of sines to find the hypotenuse of the 30-60-90 triangle by first showing how the outside triangle has angles of 45, 120, and 15 degrees.
Call the hypotenuse of the inside triangle, c, so that
(sin 15)/100 = (sin 45)/c
which leads to
c = 100 sin 45 / sin 15 = 273.2
The height of the balloon is sqrt(3)/2 times that...or 236.6 yards...
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