Find the angle of depression if an observer 150cm tall looks like a tip of his shadow which is 150√3
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Answer:
Ф=30°
Step-by-step explanation:
tanФ=height of man ÷ length of his shadow
= 150÷150√3
= 1÷3
tanФ=tan30°
Therefore angle of depression is 30°
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From the above figure, it is clear that BC||AD, therefore,
∠DAC=∠ACB=θ (Alternate angles)
We know that tanθ=OppositesideAdjacentside=ABBC
In △ABC, ∠B=900 and ∠C=θ.
Here, θ=θ, BC=1503√ m and AB=150 m, therefore,
tanθ=ABBC⇒tanθ=1501503√⇒tanθ=13√⇒tanθ=tan300(∵tan300=13√)⇒θ=300
Hence, the angle of depression is 300.