Question

at a point on a level plane, a tower subtends an angle alpha and a man, a meters tall standing on its top, subtends an angle beta. prove that the height of the tower is acot(alpha+beta)/cot alpha - cot (alpha+beta)

Answer 1

height of Tower = aCot(α + β)/((Cotα - Cot(α + β ))

Step-by-step explanation:

d = distance of point from bottom of tower

h = height of tower

Tanα  = h/d

=> d = h/Tanα

=> d = hCotα

Tan(α + β )  = (h + a)/d

=> d = (h+a)/Tan(α + β )

=> d = (h+a)Cot(α + β )

Equating

hCotα =  (h+a)Cot(α + β )

=> hCotα - hCot(α + β ) = aCot(α + β )

=> h(Cotα - Cot(α + β )) = aCot(α + β)

=> h = aCot(α + β)/((Cotα - Cot(α + β ))

Hence height of Tower = aCot(α + β)/((Cotα - Cot(α + β ))

QED

Proved

Learn more:

Prove that the height of the tower is h tan A / tan B - tan A - Brainly.in

https://brainly.in/question/11774249

The angle of elevation of the top of a tower at any point A on the ...

https://brainly.in/question/11492155