Question

From the top of tower A the sum of the angle of elevation of the top of Building B and the angle of depression of the foot of the said building is 75°. The 10.2m tower and the building lie on the same level ground and is 97m apart, find the height of Building B.

Answer 1

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Answer 2

Answer:262.85m

Step-by-step explanation:

let height of tower(AB) is h and building(CD) is h+x.

angle of elevation and depression =75°

∠k+∠l=75°

tan (k+l)=tan 75°

tan k + tan l /1-tna k*tan l=2+√3

x/97 + 10.2/97 / 1-10.2/97²

by solving x=252.65

tan l=h/97

⇒tan l =10.2/97

tank k =x/97

so height of building = x+h

⇒height of building= 252.65+10.2=262.85m