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XAT 2022 — QA & DI Question 8

Height & DistanceEasy

A tall tower has its base at point K. Three points A, B and C are located at distances of 4 metres, 8 metres and 16 metres respectively from K. The angles of elevation of the top of the tower from A and C are complementary. What is the angle of elevation (in degrees) of the tower’s top from B?

Answer & solution

  • A

    60

  • B

    30

  • 45

  • D

    We need more information to solve this.

  • E

    15

Solution

​​​​​​​

Given the distances are :
AE = 4 meters , EB = 8 meters and EC = 16 meters.
Considering the length of ED = K.
Given the angles DAE and angle DCE are complementary.
Hence the angles are A and 90 - A.
Tan(90 - A) = Cot A

tan DAE = k4 and tan DCE = tan 1DAE = k16

Hence k16 = 4k

k = 8 meters.
The angle DBE is given by

tan DBE = k8 = 1

Hence the angle is equal to 45 degrees.

XAT 2022 QA & DI Q8: A tall tower has its base at point K. Three points A, B and C are located at distances of 4 metres, 8 metres a — Solution | TheCATExam