Question

Find the height of a chimney, when it is found that on walking 100 m towards it, in a horizontal line through its base, the angle of elevation of its top changes from 45° to 60°. ​

Answer 1

Answer:

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Step-by-step explanation:

Let BC=x

⟹AC=100+x

From ΔBCD

CD=x⋯(1)

From ΔACD

tan30=

x+100

CD

sqrt3

1

=

100+x

x

⋯(2)

From (1)&(2)

⟹

3

x=(x+100)

⟹

3

x−x=100

⟹(

3

−1)x=100

⟹x=

3

−1

100

⟹x=

3

−1

100

×

3

+1

3

+1

⟹x=

2

100(

3

+1)

⟹x=50(

3

+1)

From (1)

Height of tower is x=50(

3

+1)