Question

please solve this bit.73​

Answer 1

Step-by-step explanation:

To find:

Height of the tower = h = ?

Solution:

In triangle ABC,

tan α = h/x+a

h = tan α (x+a) ....equ 1

In triangle BCD,

tan β = h/x

x = h/tan β ....equ 2

Substitute equ 2 in equ 1

h = tan α ( h/tan β + a)

h = tan α(h/tan β) + tan α(a)

h = tan α(h) + (a)(tan α)(tan β) /tanβ)

h(tanβ) = tan α(h) + a(tan α)(tan β)

h(tanβ) - tan α(h) = a(tan α)(tan β)

h(tanβ - tan α) = a(tan α)(tan β)

h = a(tan α)(tan β) / tanβ - tan α

Hence proved.

Hope it helps you:)