Question

A 6m 40cm high pole casts a shadow 4m 80cm long. Find :
(a) the length of shadow cast by another pole 12m 80cm high.
(b) the height of a pole which casts a shadow 2m 40cm.​

Answer 1

Given :-

• Height of the pole (P) = 6m 40 cm
• Length of the shadow (B) = 4m 80 cm

Solution :-

In Right angled Δ ABC formed,

Perpendicular, P = 6.40 m

Base, B = 4.80 m

Since,

$\because \rm \tan \theta = \frac{P}{B}$

Therefore,

$\therefore \mathrm{\tan \theta = \frac{6.40}{4.80}}$

$\implies \mathrm{\tan \theta = \cancel{\frac{6.40}{4.80}}}$

$\implies \boxed{\bold{\mathrm{\tan \theta = \frac{4}{3}}}}$

(a) To find :- The length of shadow cast by the another pole 12 m 80 cm high.

Solution :-

Length of the pole, P = 12.80 m

Since,

$\because \rm \tan \theta = \frac{P}{B}$

Therefore,

$\therefore \rm \tan \theta = \frac{12.80}{B}$

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., $\tan \theta$ is equal in both poles.

So, $\tan \theta = \frac{4}{3}$

Now,

$\therefore \rm \frac{4}{3} = \frac{12.80}{B}$

By Cross multiplication,

$\implies \rm 4 \times B = 3 \times 12.80$

$\implies \rm B = \frac{3 \times 12.80}{4}$

$\implies \rm B = \frac{3 \times \cancel{12.80}}{\cancel{4}}$

$\implies \rm B = 3 \times 3.2$

$\implies \rm \bf B = 9.6 m$

Hence, the length of the shadow cast by that pole is 9.6 m or 9m 60cm.

(b) To find :- The height of a pole which casts a shadow 2m 40cm.

Solution:-

Length of the shadow, B (Base) = 2m 40 cm = 2.4 m

Since,

$\because \rm \tan \theta = \frac{P}{B}$

Therefore,

$\therefore \rm \tan \theta = \frac{P}{2.4}$

Also,

$\because \rm \tan \theta = \frac{4}{3}$

So,

$\therefore \rm \frac{4}{3} = \frac{P}{2.4}$

By Cross Multiplication,

$\implies \rm 3 \times P = 4 \times 2.4$

$\implies \rm P = \frac{4 \times 2.4}{3}$

$\implies \rm P = \frac{4 \times \cancel{2.4}}{\cancel{3}}$

$\implies \rm P = 4 \times 0.8$

$\implies \rm \bf P = 3.2 m$

Hence, the height of the pole that casts that shadow is 3.2 m or 3 m 20 cm.

Answer 2

Answer:

Don't know sorry

Step-by-step explanation:

I don't understand