From the top of a lamp post of height x meters, two objects on the ground on the same side of it (and in line with the foot of the lamp post) are observed at angles of depression of 30º and 60º respectively. The distance between the objects is 32√3 m. The value of x is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 48
Let BD = y
In the triangle ABC,
tan 30º = x/(32√3 + y)
⇒ 1/√3 = x/(32√3 + y)
tan 60º = x/y
⇒ √3 = x/y
⇒ y = x/√3
from the first equation:
1/√3 = x√3/(96 + x)
⇒ 96 + x = 3x
⇒ x = 48