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The angles of depression and elevation of the top of a wall 11 m high from top and bottom of a tree are 60° and 30° respectively. What is the height of the tree?
25 m
23 m
44 m
45 m
Let DC be the wall, AB be the tree. Given that angleDBC = 30°, angleDAE = 60°, DC = 11 m tan 30°=DC/BC 1/√3=11/BC BC = 11√3m AE = BC =11√3m?(1) tan60°=ED/AE √3=ED/11√3 [? Substituted value of AE from (1)] ED =11√3×√3=11×3=33 Height of the tree = AB = EC = (ED + DC) = (33 + 11) = 44 m
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