SOLUTION: One observer at point A estimates the angle of elevation to the basket of a hot air balloon to be 55�, while another observer 100 yards away at point B estimates the angle of eleva

Question 935069: One observer at point A estimates the angle of elevation to the basket of a hot air balloon to be 55�, while another observer 100 yards away at point B estimates the angle of elevation to be 36�. How high off the ground is the basket of the hot air balloon? Round to the nearest whole number.
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
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make a triangle between basket and points A and B:
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point A supplementary angle:
180 - 55 = 125
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angle at point C, the basket:
180 - 125 - 36 = 19
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use the law of sines to find the length of side "b":
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b/sinB = c/sinC
b = sinB * c/sinC
b = sin(36) * 100/sin(19)
b = 180.541384114 yards
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make a new right triangle with a vertical side "a" directly below the basket, point B as the 90 degree point, and point A as the other vertex:
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the new angle at point C (the basket):
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180 - 55 - 90 = 35
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use the law of sines to find the length of side "a":
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a/sinA = b/sinB
a = sinA * b/sinB
a = sin(55) * 180.541384114/sin(90)
a = 147.891 yards
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answer:
height of basket above ground = 147.9 yards
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