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A street light bulb is fixed on a pole 6 m above the level of the street. If a woman of height 1.5 m casts a shadow of 3m, find how far she is away from the base of the pole

Solution:

Given, a street light bulb is fixed on a pole 6m above the level of the street.

Also, a woman of height 1.5 m casts a shadow of 3 m.

We have to find the distance between the woman and the base of the pole.

Let PQ be the height of street light bulb = 6 m

Let CD be the height of the woman = 1.5 m

Let ED be the shadow of the woman = 3 m

Let DQ be the distance between the woman and the base of the pole = x m

In △CDE and △PQE,

∠E = ∠E = common angle

∠D = ∠Q = 90°

AAA criterion states that if two angles of a triangle are respectively equal to two angles of another triangle, then by the angle sum property of a triangle their third angle will also be equal.

By AAA criterion, △CDE ⩬ △PQE

By the property of similarity,

The corresponding sides are proportional.

So, ED/EQ = CD/PQ

3/(3 + x) = 1.5/6

On cross multiplication,

3(6) = 1.5(3 + x)

18 = 4.5 + 1.5x

1.5x = 18 - 4.5

1.5x = 13.5

x = 13.5/1.5

x = 9 m

Therefore, the woman is at a distance of 9 m from the base of the pole.

✦ Try This: A street light bulb is fixed on a pole 8 m above the level of the street. If a woman of height 2 m casts a shadow of 3.8m, find how far she is away from the base of the pole.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 6

NCERT Exemplar Class 10 Maths Exercise 6.4 Problem 8

A street light bulb is fixed on a pole 6 m above the level of the street. If a woman of height 1.5 m casts a shadow of 3m, find how far she is away from the base of the pole

Summary:

A street light bulb is fixed on a pole 6 m above the level of the street. If a woman of height 1.5 m casts a shadow of 3m, she is 9 m away from the base of the pole

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