A 1.6 M Tall Girl Stands at a Distance of 3.2 M from a Lamp-post and Casts a Shadow of 4.8 M on the Ground. Find the Height of the Lamp-post by Using (I) Trigonometric Ratios (Ii) Property of Similar Triangles. - Mathematics

A 1.6 m tall girl stands at a distance of 3.2 m from a lamp-post and casts a shadow of 4.8 m on the ground. Find the height of the lamp-post by using (i) trigonometric ratios (ii) property of similar triangles.

Solution

Let AC be the lamp post of height h

We assume that ED 1.6 m, BE = 4.8 m and EC = 3.2 m

We have to find the height of the lamp post

Now we have to find the height of lamp post using similar triangles.

Since triangle BDE and triangle ABC are similar.

(AC)/(BC) = (ED)/(BE)

h/(4.8 + 3.2) = 1.6/(BE)

h =  8/3

Again, we have to find height of lamp post using trigonometric ratios.

=> tan theta = 1.6/4.8

=> tan theta  = 1/3

Again in  ΔABC

=> tan theta = h/(4.8 + 3.2)

=> 1/2  = h/8

h = 8/3

Hence the height of lamp post is 8/3 m

Concept: Heights and Distances
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APPEARS IN

RD Sharma Class 10 Maths
Chapter 12 Trigonometry
Exercise 12.1 | Q 21 | Page 31