What is the angle of elevation of the sun when the length of the shadow of a pole 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.

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?

An aeroplane at an altitude of 200 metres observes the angles of depression of opposite points on the two banks of a river to be 45° and 60°. Find the width of the river.

Let the position of the aeroplane be A, B and C be two points on the two banks of a river such that the angles of depression at B and C are 45° and 60° respectively. Let BD = x m, y m andAD = 200 m.

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∘

Open in App