SOLUTION: (We are given the answer of 48 yards and need to find the proper Trig. formula and write out the problem in detail but I'm lost on where to even start Please Help!) One observer

Question 935876: (We are given the answer of 48 yards and need to find the proper Trig. formula and write out the problem in detail but I'm lost on where to even start Please Help!)
One observer estimates the angle of elevation to the basket of a hot air balloon to be 55 degrees, while another observer 100 yards away estimates the angle of elevation to be 36 degrees. How high off the ground is the basket of the hot air balloon? Round to the nearest whole number.

Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Let the ground distance from one point be x.
Let's name this point Q
We have a triangle ABC
AQ= x
BQ = 100-x
Vertical height BQ = y
the distance from other point will be 100-x
Tan 55 = BT / x
x= BT/tan 55...............................(1)
tan 36 = BT /(100-x)
100-x= BT/tan 36
x= 100-(BT/tan 36)................................(2)
Equate (1) & (2)
BT/tan 55=100-(BT/tan 36)
0.7*BT = 100-1.376 *BT
0.7*BT +1.376 *BT=100
2.076BT =100
BT = 48.16

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