The shadow of a tower standing on level ground is found to be 40 m longer when the Sun's altitude is 30° than when it was 45°. Find the height (in meters) of the tower.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. .
Let the height of a tower AB be H meters
Given that
The elevation angle of Sun changes from 30º to 45º.
The distance of CD = 40 m
In triangle ABC,
tan 45º = H/BC
BC = H meters
In triangle ABD,
⇒ tan 30º = H/(H + 40)
⇒ 1/√3 = H/(H + 40)
⇒ H + 40 = H√3
⇒ H = 40/(√3 - 1)
⇒ H = 40 (√3 + 1)/2
⇒ H = 20 (√3 + 1) meters