Question

A 8 m 40 CM high vertical pole casts a shadow 4 m 80 CM long. Find at the same time - (a) the height of a pole which casts a shadow 4 m long.
(b) the length of the shadow cast by another pole 12 m 25 cm long high.​

Answer 1

Answer:

Given :

Height of the pole (P) = 8m 40 cm • Length of the shadow (B) = 4m 80 cm

Solution:

In Right angled A ABC formed,

Height of the pole, Perpendicular, P = 8.40 m

Length of the shadow, Base, B = 4.80 m

Since,

tan 0 = P/B

Therefore,

tan 0 =8.40/4.80

= tan 0 = 3/2

(a) To find :- The height of a pole which casts a shadow 4m long.

Solution:

Length of the shadow, Base, B = 4m

Since,

tan 0= P/B

Hence, the sun is casting the same angle of elevation of light, so angle of suspension of shadow formed of all poles is equals, i.e., tan 0 is equal in both poles.

So,

Tan 0 = 3/2

Therefore,

3/2= P/4

By Cross Multiplication,

2 x P = 4 x 3

P = 4×3/2

P = 2 x 3

P = 6m

Hence, the height of the pole that casts that shadow is 6 m.

(b) To find - The length of shadow cast by the another pole 12 m 25 cm high.

Solution :

Length of the pole, P = 12.25 m

Since,

... tan 0 = P B

Therefore,

... tan 0 = 12.25 B

Also,

... tan 0= 3/2

So,

3/2 = 12.25/B

By Cross multiplication,

3 x B= 2 x 12.25

B = 2×12.25/3

B = 24.50/3

B= 8.16m

Hence, the length of the shadow cast by that pole is 8.16 m or 8m 16cm.