Question

A vertical tower standing on a horizontal plane is surmounted by a vertical flagstaff. At a point 100 m away from the foot of the tower, the angle of elevation of the top and bottom of the flagstaff are 54° and 42° respectively. Find the height of the flagstaff. Give your answer correct to nearest metre.

Answer 1

In ΔPAB,

`(AB)/(PA) = tan 42^circ`

`(AB)/100 = 0.9004`

`\implies` AB = 90.04 m

In ΔPAF,

`(AF)/(PA) = tan 54^circ`

`(AF)/100 = 1.3764`

`\implies` AF = 137.64 m

FB = 137.64 m – 90.04 m

= 47.60 m

= 48 m