Question

a flagstaff of height H stands on the top of a building if the angles of devertion of the top and bottom of the flagstaff have measure alpha and beta are respectively from a point on the ground prove that the height of the building is h tan beta ÷ tan alpha - tan beta​

Answer 1

Step-by-step explanation:

see the attachment

Thank you

Answer 2

The height of the building is

$H = \frac{h \tan \beta}{\tan \alpha - \tan \beta}$

Step-by-step explanation:

Height of building = H

height of flag = h

∠ ADC = α & ∠ BDC = β

From Δ BCD

$\tan \beta = \frac{H}{x}$

$x = \frac{H}{\tan\beta}$ --------- (1)

From Δ ADC

$\tan \alpha = \frac{y + h}{x}$

$x = \frac{H + h}{\tan\alpha}$ --------- (2)

Equation (1) = Equation (2)

$\frac{H}{\tan\beta}$ $= \frac{h + H}{\tan \alpha}$

By solving these equation we get,

$H \tan \alpha = h\tan \beta + H \tan \beta$

$H ( \tan \alpha - \tan \beta) = h \tan \beta$

$H = \frac{h \tan \beta}{\tan \alpha - \tan \beta}$  

This is the height of the building. Thus it is prove that height of the building  $H = \frac{h \tan \beta}{\tan \alpha - \tan \beta}$