Question

A person of height 6 feet standing in the north direction of a lamp-post has 30 feet shadow on the horizontal ground. He then walks 144 feet to the east and observes that his shadow is 78 feet in length. Find the height of the lamp-post.

Answer 1

Step-by-step explanation:

PQ = h is the lamp post; AL the man due South of it and of height 6 ft. and AC = 24 ft. is the length of the shadow. After walking 300 ft. Eastwards he comes to B and now the length of shadow is BD =30 ft.

Now let AP = x and BP = y, AC = 24, BD = 30.

From Δ

′

s QPC and LAC

We have

6h

= 24/24+x

∴x=4(h−6) ...(1)

Similarly from Δ s

QPD and MBD6h

= 30y+30

∴y=5(h−6) ...(2)

From (1) and (2), we get

h= 424+x

= 5y+30

∴y= 45 x.

Again from rt. angled triangle PAB in which

∠PAB=90

oPB 2 =PA

2 +AB 2 or y

2 −x 2 =(300) 2

Putting for y and x from (1) and (2) in (3), we get

(h−6)

2

[25−16]=300

2

=9.100 2

∴h−6=100 or h=6+100=106ft.

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