Question

A 1.6 m tall girl stands at a distance of 5.2 m from a lamp-post and casts a shadow of 6.8 m on the

ground. Find the height of the lamp-post by Using Trigonometric ratios.​

Answer 1

(i) Using trigonometric ratios.

Let AB be the height of lamp post.

Now, in right △CDE,

⇒tanθ=

DC

ED

=

4.8

1.6

=

3

1

⟶(1)

In , △ACB,

⇒tanθ=

BC

AB

=

3.2+4.8

AB

=

8

AB

⟶(2)

From (1)&(2) we get

⇒

3

1

=

8

AB

⇒AB=

3

8

=2.67m

∴ Height of the lamp post =2.67m

(ii) Using similar triangles :

In △CDE&△CBA

i)∠CDE=∠CBA=90°

ii)∠DCE=∠BCA (Common)

∴△CDE∼△CBA ( By AA similarities )

Hence,

AB

DE

=

BC

CD

⇒AB=

CD

DE×BC

=

4.8

1.6×8

=

3

8

=2.67m

∴ Height of lamp post =2.67m.

Hence, the answer is 2.67.

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Answer 2

Answer:

We are given that,

Height of the girl = 1.6 meters

Distance of girl from the lamp post = 3.2 meters

Distance of girl from the shadow = 4.8 meters

From the figure,we will find the angle θ using trigonometric form of the angles,

\tan \theta=\frac{Perpendicular}{Base}tanθ=

Base

Perpendicular

i.e. \tan \theta=\frac{1.6}{4.8}tanθ=

4.8

1.6

i.e. \tan \theta=0.33tanθ=0.33

i.e. \theta=\arc tan 0.33θ=\arctan0.33

i.e. θ = 18.26°

The height of the lamp post is given by,

\tan \theta=\frac{Perpendicular}{Base}tanθ=

Base

Perpendicular

i.e. \tan 18.26=\frac{x}{3.2+4.8}tan18.26=

3.2+4.8

x

i.e. \tan 18.26=\frac{x}{8}tan18.26=

8

x

i.e. x=8\times \tan 18.26x=8×tan18.26

i.e. x=8\times 0.33x=8×0.33

i.e. x = 2.64 meters.

Thus, the height of the lamp post is 2.64 meters.

Answer 3

Answer:

We are given that,

Height of the girl = 1.6 meters

Distance of girl from the lamp post = 3.2 meters

Distance of girl from the shadow = 4.8 meters

From the figure,we will find the angle θ using trigonometric form of the angles,

\tan \theta=\frac{Perpendicular}{Base}tanθ=

Base

Perpendicular

i.e. \tan \theta=\frac{1.6}{4.8}tanθ=

4.8

1.6

i.e. \tan \theta=0.33tanθ=0.33

i.e. \theta=\arc tan 0.33θ=\arctan0.33

i.e. θ = 18.26°

The height of the lamp post is given by,

\tan \theta=\frac{Perpendicular}{Base}tanθ=

Base

Perpendicular

i.e. \tan 18.26=\frac{x}{3.2+4.8}tan18.26=

3.2+4.8

x

i.e. \tan 18.26=\frac{x}{8}tan18.26=

8

x

i.e. x=8\times \tan 18.26x=8×tan18.26

i.e. x=8\times 0.33x=8×0.33

i.e. x = 2.64 meters.

Thus, the height of the lamp post is 2.64 meters.

Answer 4

Answer:

We are given that,

Height of the girl = 1.6 meters

Distance of girl from the lamp post = 3.2 meters

Distance of girl from the shadow = 4.8 meters

From the figure,we will find the angle θ using trigonometric form of the angles,

\tan \theta=\frac{Perpendicular}{Base}tanθ=

Base

Perpendicular

i.e. \tan \theta=\frac{1.6}{4.8}tanθ=

4.8

1.6

i.e. \tan \theta=0.33tanθ=0.33

i.e. \theta=\arc tan 0.33θ=\arctan0.33

i.e. θ = 18.26°

The height of the lamp post is given by,

\tan \theta=\frac{Perpendicular}{Base}tanθ=

Base

Perpendicular

i.e. \tan 18.26=\frac{x}{3.2+4.8}tan18.26=

3.2+4.8

x

i.e. \tan 18.26=\frac{x}{8}tan18.26=

8

x

i.e. x=8\times \tan 18.26x=8×tan18.26

i.e. x=8\times 0.33x=8×0.33

i.e. x = 2.64 meters.

Thus, the height of the lamp post is 2.64 meters.