Question

A 6m and 40cm high pole casts a shadow 4m 80cm long find:
i, the length of shadow cast by another pole 12m 80cm high.
ii, the height of a pole which casts a shadow 2m 40cm​
step by step explanation plz answer if u know

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., tanθ

is equal in both poles.

So,

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

Now,

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

By Cross multiplication,

$\implies \rm 4 \times B = 3 \times12.80$

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

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

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

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

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,

$\implies \rm 3 \times P = 4 \times2.4$

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

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

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

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

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