Asked by Alex

Justin is riding in a hot air balloon, directly over Ben, who is standing on the ground. Justin spots Patti on the ground at an angle of depression of 27 degrees. The balloon rises 35m. Now the angle of depression to Patti is 36 degrees. How far is Patti from Ben?
Answered by scott
h = initial balloon height , d = Patti/Ben distance

h / d = tan(27º) ... h / tan(27º) = d

(h + 35) / d = tan(36º) ... (h + 35) / tan(36º) = d

(h + 35) tan(27º) = h tan(36º) ... 35 tan(27º) = h [tan(36º) - tan(27º)]

solve for h , then substitute back to find d
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