SOLUTION: 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 d

Question 821549: 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 TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
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triangle ABC abc:
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c = 300 ft
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A = 180 - 55 = 125 degrees
B = 36 degrees
C = 180 - 125 - 36 = 19
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use the law of sines to find the range from the second observer to the basket:
a/sinA = c/sinC
a/sin(125) = 300/sin(19)
a = sin(125)*300/sin(19)
a = range = 754.8208 ft
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use sine(B) to find the height of the basket:
sin = opp/hyp
sin(36) = height/range
height = sin(36)*range
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answer:
height = 444 ft
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