Question

From her elevated observation post 300m away, a naturalist spots a troop of baboons high up in a tree. Using the small transit attached to her telescope, she finds the angle of depression to the bottom of this tree is 30°, while the angle of elevation to the top of the is 60°. The angle of elevation to the troop of baboons is 45°. Use this information to find the height of the observation post, the height of baboons tree and the height of the baboons above the ground.​

Answer 1

(A) height of elevation post = 100√3 m

(B) height of tree = 400√3 m

(C) height of baboons above ground = 100√3 ( √3 + 1 ) m

Let CD = AB =h metres, FE = h1 metres, DE = h2 metres

AD = BC = 300 M

(A) in triangle ABC,

•    tan 30 = h/300
• ⇒ h = 300/√3 = 100√3 m

(B) in triangle ADF,

•    tan 60 = FD/300
• ⇒ FD = 300√3 m

• CF = height of tree = DC + DF = 100√3 + 300√3 m = 400√3 m

(C) in triangle AED,

•    tan 45 = h2/300
• ⇒ h2 = 300 m

• CE = CD + DE = 300 + 100√3 = 100 ( 3 + √3 ) = 100√3 ( 1 + √3 ) m