Question

The shadow of a tower is equal to its height . The sun’s altitude is​

Answer 1

Let the length of shadow =x

⇒ Height =x

      Angle =A

so, tanA=xx=1

      tanA=tan450

so, A=450

Hence, the answer is 450.

Answer 2

The sun's angle of elevation is 45°.

Given:

• The shadow of a tower is equal to its height .

To find:

• Angle of elevation of sun .

Solution:

Concept to be used: Apply trigonometric ratio.

Step 1:

Draw the diagram for the suitation, as shown in attachment.

Here Height of tower is AB (Perpendicular)

Length of shadow is AC (Base)

Step 2:

Apply trigonometric ratio.

As

$tan \: \theta = \frac{ \text{side \: opposite \: to \: angle}}{\text{side \: adjacent \: to \: angle}} = \frac{AC}{AB}$

here,

AC= AB

So,

$tan \: \theta = 1$

or

$tan \: \theta = tan \: 45^{\circ}$

or

$\bf \theta = 45^{\circ}$

Thus,

Angle of elevation of sun is 45°.

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