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

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 

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.

Let θ be the angle of elevation of the sun. Let AB be the vertical pole of height h and BC be the shadow of equal length h.

Here we have to find the angle of elevation of the sun.

We have the corresponding figure as follows.

So we use trigonometric ratios to find the required angle.

In a triangle ABC

`=> tan theta = (AB/(BC)`

`=> tan theta = h/h`

`=> tan theta = 1

`=> theta = 45^@`

Hence the angle of evevation of sun is  45°

Concept: Heights and Distances

  Is there an error in this question or solution?

If the height of a vertical pole is equal to the length of its shadow on the ground, the angle of elevation of the sun is a 0∘ b 30∘ c 45∘ d 60∘

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