A person standing on the bank of a river observes that the angle of elevation of the top of a tree o...........

Quantitative Aptitude ( CCS) Trignometry

A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank is 45⁰. When he moves 20m away from the bank, he finds the angle of elevation to be 30⁰. Find the height of the tree.

10(√3 + 1)m

15√3m

200(√3 + 1)m

10(√3 - 1)m

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Explanation:

Let AB = x is the tree and AC = y is the river.
Let the angle of elevation at point C is 45⁰ and at point D is 30⁰ s.t. CD = 20 m
In ΔACB
Height & Distances
tan 45⁰ = x/y ⇒ 1 = x/y ⇒ x = y ……(1)
In ΔADB, tan 30⁰ = AB/AD
⇒ 1/√3 = x/ (20 + y)
⇒ 1/√3 = x/ (20 + x) [ ? of (1)]
⇒ 20 + x = √3x
⇒ (√3-1)x = 20
⇒ x = 20/(√3 - 1)
= 20/(√3 - 1) x (√3 + 1)/(√3 + 1)
= [20(√3 + 1)]/3-1
⇒ x = [20(√3 + 1)]/2
⇒ x = 10(√3 + 1)m