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?
22 m
44 m
33 m
None of these
Explanation:
Let DC be the wall, AB be the tree.
Given that $\angle$DBC = 30°, $\angle$DAE = 60°, DC = 11 m
tan30°=$\dfrac{DC}{BC}$
=>$\dfrac{1}{\sqrt{3}}=\dfrac{11}{BC}$
BC = 11√3 m
AE = BC =11√3 m ⋯(1)
tan60°=$\dfrac{ED}{AE}$
=>√3=$\dfrac{ED}{11\sqrt{3}}$ [∵ 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
Let DC be the wall, AB be the tree.
Given that $\angle$DBC = 30°, $\angle$DAE = 60°, DC = 11 m
tan30°=$\dfrac{DC}{BC}$
=>$\dfrac{1}{\sqrt{3}}=\dfrac{11}{BC}$
BC = 11√3 m
AE = BC =11√3 m ⋯(1)
tan60°=$\dfrac{ED}{AE}$
=>√3=$\dfrac{ED}{11\sqrt{3}}$ [∵ 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