Question

From elevated observation post 300 m away, a naturalist time sports a troops of babbons 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° whole the angle of elevation to the top of the tree is 60°. The angle of elevation of the troop of babbon's tree is 45°. Use this information to find (a) the height of elevation post, (b) the height of babbons' tree, (c) the height of the babbons above the ground.

Answer 1

Answers :-

(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 metresAD = 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 mCF

= height of tree = DC + DF

= 100√3 + 300√3 m

= 400√3 m

(C) in triangle AED, 

 tan 45 = h2/300

⇒ h2 = 300 mCE

= CD + DE = 300 + 100√3

= 100 ( 3 + √3 )

= 100√3 ( 1 + √3 ) m

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