Question

A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height h .At a point on the plane the angle of elevation of the bottom and the top of the flag staff are x and p respectively prove that the height of the tower is ( h tan x/ tan p - tan x ) ? ​

Answer 1

Answer:

Let height be y ΔOAC

tanθ=

B

P

tanβ=

OA

CA

tanβ=

x

y+h

(y+h)→ Let AB, AB+BC

Let OA→ x

x=[

tanβ

y+x

]

Consider ΔOAB

tanα=

x

y

=

Base

perpendicular

x=

tanα

y

tanα

y

=

tanβ

y+h

ytanβ=tanαy+tanαh

ytanβ−tany=tanαh

y(tanβ−tanα)=tanαh

y=

tanβ−tanα

htanα

This proved.