The angles of depression and elevation of the top of a wall 11 m high from top and bottom of a tree ...........

Quantitative Aptitude ( CCS) Trignometry

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

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Explanation:

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