A man 18 m high stands at a distance of 36 m from a lamp post and casts a shadow of 54 m on the grou...

Question

A man 18 m high stands at a distance of 36 m from a lamp post and casts a shadow of 54 m on the ground Find the height of the lamp post

Accepted Answer

Solution The angle produced by the line of sight and the horizontal plane for an object above the horizontal is known as the angle of elevation As seen in the image below we must take into consideration two right angled triangles to get the height of the lamp post Consider AB as the lamp post CD is the height of man BD is the distance of man from the foot of the lamp FD is the shadow of man Construct CE parallel to DB Take AB x and CD 18 m EB CD 18 m AE x 18 Shadow FD 54 m In right AEC tan AECE Substituting the values tan x 18 36 1 In right CDF tan CDFD Substituting the values tan 1854 13 2 Using both the equations x 18 36 13 So we get 3x 54 36 3x 36 54 90 By division x 93 30 Hence the height of lamp post is 3 m

ML Aggarwal Solutions Class 10 Mathematics Solutions for Heights and Distances Exercise 20 in Chapter 20 - Heights and Distances