Question

A 7m long flagstaff I'd fixed on the top of tower standing on the horizontal plane from point on the ground the angle of elevation of the top and bottom of the flagstaff are 60 degrees and 45degree respectively find the height of the tower correct to one place of decimal

Answer 1

Hope it helps you!!!!!!

Answer 2

Given,

The length of the flagstaff, AB = 7m

A reference point on the ground, D.

The angle of elevation to the top of the tower = 60°

The angle of elevation to the bottom of the tower = 45°

To find,

The height of the tower, BC.

Solution,

In the ΔADC,

tan60 = AC/DC = √3

         ⇒ (AB+BC)/DC = √3

         ⇒ 7 + BC = √3 DC  ______ (1)

In ΔBCD,

sin45 = BC/DC = 1

         ⇒ BC = DC

from equation (1) and (2) we get

7 + BC = √3BC

⇒ 1.73BC - BC = 7

⇒ 0.73BC = 7

⇒ BC = 7/0.73 = 9.58 m

∴ The height of the tower is 9.58 m.