Question

the angle of elevation of the top of a tower at point on the ground is 30.if on walking 20 meters toward the tower the angle of elevation becomes 60,the height of the tower is
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Answer 1

Firstly, We know that the Elevation of the top of the tower from the level ground is 30⁰.

Let the height of the Tower be h and the distance b/w the base of the tower and the second point be x m.

→ tan ∅ = P/B

→ tan 30⁰ = h/x

→ 1/√3 = h/(x + 20)

→ h = (x+20)/√3 [1]

Now, we also know that After moving 20 metres towards the Tower, the angle of elevation becomes 60⁰.

→ tan 60⁰ = P/B

→ √3 = h/x

→ √3x = (x+20)/√3 [From [1] ]

→ 3x = (x + 20)

→ 3x - x = 20

→ 2x = 20

→ x = 20/2

→ x = 10

Finally, we can find the Height of the Tower by putting value of Base of the tower.

→ tan 60⁰ = h/x

→ √3 = h/10

→ h = 10√3

Hence,

The Height of the tower will be 10√3 m.