Trigonometry
posted by Allison on .
Karla is riding vertically in a hot air balloon, directly over a point P on the ground. Karla spots a parked car on the ground at an angle of depression of 30o. The balloon rises 50 meters. Now the angle of depression to the car is 35°. How far is the car from point P?

We form 2 similar rt. triangles:
Triangle #1.
X = Hor. side = dist. from P to the car.
Yi = Ver. side.
A = 30o.
Triangle #2.
X = Hor. side = Dist. from P to the car.
Y2 = Y1+50 = Ver. side.
A = 35o.
Use aw of Sines.
sin30/Y1 = sin35/(Y1+50).
Cross multiply:
(Y1+50)sin30 = Y1*sin35
Y1/2+25 = 0.574Y1
Multiply both sides by 2:
Y1+50 = 1.148Y1
1.148Y1Y1 = 50
0.148Y1 = 50
Y1 = 337.8 m.
tan30 = Y1/X = 337.8/X
X = 337.8/tan30 = 585 m. 
714 feet away

I gave up.