What is the angle of elevation of the sun when the length of the shadow of a vertical tower is equal to its height?

Find the angle of elevation of the sum sun's altitude when the length of the shadow of a vertical pole is equal to its height

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Solution:

Consider AB as the pole and CB as its shadow

θ is the angle of elevation of the sun

Take AB = x m and BC = x m

We know that

tan θ = AB/CB = x/x = 1

So we get

Hence Proved

A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.

Let height of the pedestal BD be h metres, and angle of elevation of C and D at a point A on the ground be 60° and 45° respectively.It is also given that the height of the statue CD be 1.6 mi.e.,    ∠CAB = 60°,∠DAB = 45° and CD = 1.6mIn right triangle ABD, we have

Hence, the height of pedestal