SOLUTION: Math gr 10 geometry sine law? Sara is riding a hot air balloon directly over John who is standing on the ground. Sara spots pat on the ground at an angle of depression of 28 degre

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Question 337340: Math gr 10 geometry sine law?
Sara is riding a hot air balloon directly over John who is standing on the ground. Sara spots pat on the ground at an angle of depression of 28 degrees. The balloon rises 34 m and now the angle of depression to pat is 35 degrees. How far is pat from John.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
let h="initial height of balloon" and d="Pat to John distance"

d/h = tan(62º) ___ d/tan(62º) = h

d(h+34) = tan(55º)

substituting ___ d{[d/tan(62º)]+34} = tan(55º) ___ (d^2)/tan(62º) + 34d = tan(55º)

d^2 + 34[tan(62º)]d = [tan(55º)][tan(62º)] ___ d^2 + 34[tan(62º)]d - [tan(55º)][tan(62º)] = 0

use quadratic formula to find d