Question

A vertical tower AT standing on a horizontal plane is observed from two points P and Q in the plane. P and Q are 20m and 70m respectively from the base of the tower(A). The angle of elevation of the top of the tower from P is 2θ and from Q is θ. Find the height of the tower

Answer 1

such a big question and you had given only five points I am not interested at all

Answer 2

Given:

• P and Q are 20m and 70m respectively from the base of the tower(A).

• The angle of elevation of the top of the tower from P is 2θ and from Q is θ.

To find:

The height of the tower.

Solution:

1) Let the height of the tower is h.

2) The ratio for the point P is

• Tan 2Ф = h/20

3) The ratio for the point Q is

• Tan Ф = h/70

• h = 70 TanФ

4) Putting in other equation

• 2TanФ/1-Tan²Ф = 70 TanФ /20

• 2/1-Tan²Ф = 7/2

• 4 = 7 - 7Tan²Ф

• 7tan²Ф = 3

• TanФ =√3/√7

5) Now putting the value of TanФ

• h = 70 √3/√7

• h = 10√21

• h = 10×4.583

• h = 45.83 m.

The height of the tower is 45.83 m.