The angle of elevation of the top of a tower from point A on the ground is 300 On moving a distance ...........

Quantitative Aptitude ( CCS) Trignometry

The angle of elevation of the top of a tower from point A on the ground is 30⁰. On moving a distance of 40m towards the foot of the tower, the angle of elevation increases to 45⁰. Find the height of the tower.

48.6m

42.84m

54.64m

58.76m

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Explanation:

Let CD is the tower of height ‘x’ m and A, B are the points where the angles of elevation are 30⁰ and 45⁰ respect.
In Δ BCD, tan 45⁰ = DC/BC
Height & Distances
⇒ 1 = x/BC ⇒ BC = x ………(1)
In ΔACD, tan 30⁰ = CD/AC
⇒ 1/√3 = x/(40+x)
⇒ 40+x = √3x
⇒ (√3 - 1)x = 40
⇒ x = 40/(√3-1) = 40/(√3-1) x (√3+1)/(√3+1)
⇒ x = 20 (√ + 1) = 54.64 m