A and B are standing on ground 50 meters apart. The angles of elevation for these two to the top of a tree are 60° and 30°. What is height of the tree?
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In ∆PBQ, tan 60° = PQ/BQ
Therefore, BQ = PQ/√3
In ∆PAQ, tan 30° = PQ/AQ
Therefore, 1/√3 = PQ/50 + BQ
PQ = 50 + BQ/√3
= 50 + PQ/√3 /√3
= 50√3 + PQ / √3 × √3
Therefore, 3PQ = 50√3 + PQ
Therefore, PQ = 25√3m = Height of the tree.
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