Question

The angle of elevation of the top of a tower from a point on the ground ,which is 30m away from the foot of the tower is 30°.Find the height of the tower​

Answer 1

Answer:

Let PR be the tower and PQ be the ground.

Let point Q be at a distance of 30 m from the tower

Given 30

o

is the angle of elevation

∴tan30

∘

=

PQ

PR

⇒PR=PQtan30

∘

⇒PR=

3

30

⇒PR=10

3

m

∴ Height of the tower is 10

3

m.

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Answer 2

Answer:

We have to find the height of the tower.

Let us consider the height of the tower as AB, the distance between the foot of the tower to the point on the ground as BC.

In ΔABC, trigonometric ratio involving AB, BC and ∠C is tan θ.

tan C = AB/BC

tan 30° = AB/30

1/√3 = AB/30

AB = 30/√3

= (30 × √3) / (√3 × √3)

= (30√3)/3

= 10√3

Height of tower AB = 10√3 m.