Question 933509: Joel wants to determine the height of a hot air balloon that is sitting on the ground. Using a surveyor's transit that is 5 feet above the ground he stands at a point A and measures the angle of elevation of the top of the balloon as 30º. He then walks 60 feet straight toward the ballon to a point B and again using the transit measures the angle of elevation of the top of the ballon as 45º. As part of your solution draw a picture illustrating this situation, marking clearly all known angles and distances and any variable(s) used in solving the problem. State clearly any equation(s) used (there must be at least one). Then find the height, h, of the balloon.
Real confused here please help
Thank you
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Joel wants to determine the height of a hot air balloon that is sitting on the ground. Using a surveyor's transit that is 5 feet above the ground he stands at a point A and measures the angle of elevation of the top of the balloon as 30º. He then walks 60 feet straight toward the ballon to a point B and again using the transit measures the angle of elevation of the top of the ballon as 45º. As part of your solution draw a picture illustrating this situation, marking clearly all known angles and distances and any variable(s) used in solving the problem. State clearly any equation(s) used (there must be at least one). Then find the height, h, of the balloon.
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Draw the picture::
You have a 30-60 degree right triangle
and a 45-45 degree right triangle
where the height of each = balloon height + 5 ft
Find the height of the 2 triangles:
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Equation:
tan(30) = h/(h+60 ft)
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1/sqrt(3) = h/(h+60)
sqrt(3)h = h+60
0.7312h = 60
h = 81.96 ft
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height of balloon = 81.96 + 5 = 86.96 ft
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Cheers,
Stan H.
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