There is a cliff 80 m high on the bank of a lake A man is sitting on the cliff He looks at a bird in...........

Quantitative Aptitude ( CCS) Trignometry

There is a cliff 80 m high on the bank of a lake. A man is sitting on the cliff. He looks at a bird in the sky and the angle of elevation is formed to be of 30⁰. When he looks at the shadow of the bird in the lake, the angle of depression is 60⁰. Find the height of the bird from the lake surface.

320/3 m

454 m

250/3m

150/7m

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Explanation:

AB is the cliff and the man is sitting at B. Let C is the position of the bird and D is its shadow.
In ΔADB, tan 60⁰ = AB/AD
Height And Distances Solved
→ √3 = 80/AD
→ AD=80/√3 m
Now BE = AD = 80/√3 m
In ΔBEC, tan 30⁰= CE/BE
→ 1/√3 = CE/(80/√3)
→ CE=80/3 m
∴ The height of the bird = DC = DE +CE
= 80 + 80/3 m = 320/3 m