A 10 m long flagstaff is fixed on the top of a tower on the horizontal plane From a point on the gro...........

Quantitative Aptitude ( CCS) Trignometry

A 10 m long flagstaff is fixed on the top of a tower on the horizontal plane. From a point on the ground, the angles of elevation of the top and bottom of the flagstaff are 60⁰ and 45⁰ respectively. Find the height of the tower.

5(√3 + 1)m

5(√3 + 3)m

10(√3 - 1)m

10(√3 + 1)m

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Explanation:

Let AB is the tower of height x m and BC is the flagstaff of height 10 m.
Let D be the point from where the angles of elevation are 45⁰ and
60⁰ such that ∠BDA = 45⁰ and ∠CDA = 60⁰
Height & Distances
In ΔDAB, tan 45⁰ = AB/AD
⇒ 1 = x/AD ⇒ AD = x
In ΔDAC, tan 60⁰ = AC/AD
⇒ √3 = (10+x)/x
⇒ √3x = 10+x
⇒ (√3-1)x = 10
⇒ x = 10/(√3 - 1) = 10/(√3 - 1) x (√3 + 1)/(√3 + 1)
⇒ x = 5(√3 + 1)