The angle of elevation of a cliff from a point A on the ground and from point B ,50m vertically - Maths - Some Applications of Trigonometry

Question

The angle of elevation of a cliff from a point A on the ground and
from point B ,50m vertically above point are alpha and beta
respectively The height of the cliff in m is?

Ajanta Trivedi · Accepted Answer

<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/images/pic1(29)%20png">
let the height of the cliff be PQ = h
m
the angle of elevation from point A is ∠PAQ=α
the angle of elevation from point B is
∠PBC=β  and AB = 50 m
let the point A is at distance of x m from the foot of the
cliff
in the right angled triangle PAQ;
tanα=PQAQ=hx⇒x=h cotα  (1)
now in the right angled triangle PBC;
tanβ=PCBC=PQ-CQAQtanβ=h-50xh-50=xtanβh=50+xtanβh=50+h
cotα tanβh(1-cotα tanβ)=50h 1-1tanα
tanβ=50h tanα-tanβtanα=50h=50
tanαtanα-tanβ

hope this helps you

The angle of elevation of a cliff from a point A on the ground and from point B ,50m vertically above point are alpha and beta respectively .The height of the cliff in m is?