A person was standing on a road near a mall. He was 1215 m away from the mall and able to see the top of the mall from the road in such a way that the top of a tree, which is in between him and the mall, was exactly in line of sight with the top of the mall. The tree's height is 20 m and it is 60 m away from him. How tall (in m) is the mall?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e 405.
Given:
Distance between mall and person = 1215 m
Distance between tree and person = 60 m
Height of tree = 20 m
Concept used:
Using the concept of trigonometric ratios
tanθ = (Perpendicular)/(Base)
Let the height of the mall be AB
In ΔDEC,
tanθ = DE/CE
⇒ tanθ = 20/60
⇒ tanθ = 1/3
In AABC,
tanθ = AB/BC
⇒ 1/3= AB/1215
⇒ AB = 405 m
Thus,
The height of the mall is 405 m.