Question

the length of shadow of a pole having 20 m height is 20✓3 m. find the length of the shadow of a pole of height 25✓3 m at the same time.​

Answer 1

Answer:

I have solved the question.

Answer 2

The length of the shadow of the pole is 75 metres.

Given:

• The length of shadow of a pole having 20 m height is 20✓3 m.

To find:

• Find the length of the shadow of a pole of height 25✓3 m at the same time.

Solution:

Concept/Formula to be used:

• Calculate angle of elevation form.
• Find the length of shadow.

Step 1:

Calculate the angle of elevation.

ATQ,

Height of pole :$\bf AB = 20 \: m$

Length of shadow: $\bf BC=20 \sqrt{3} \: m$

*See the attachment 1.

The angle of elevation

$\bf tan \: \theta= \frac{AB}{CB}$

$tan \: \theta= \frac{20}{20 \sqrt{3} }$

$tan \: \theta= \frac{1}{ \sqrt{3} }$

$\bf \theta= {30}^{ \circ}$

Thus,

Angle of elevation of sun is 30°.

Step 2:

Calculate the length of shadow of pole.

ATQ,

*See the attachment 2.

Height of pole: $\bf AB=25 \sqrt{3} \: m$

Apply tangent trigonometric ratio on ∆ABC in fig 2.

$tan \: {30}^{ \circ} = \frac{25 \sqrt{3} }{CB }$

$CB = \frac{25 \sqrt{3} }{ \frac{1}{ \sqrt{3} } }$

$CB= 25 \sqrt{3} \times \sqrt{3}$

$CB = 25 \times 3$

$\bf CB = 75 \: m$

Thus,

The length of shadow of pole is 75 metres.

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