Question

A pole that is 2.6 m tall casts a shadow that is 1.03 m long. At the same time, a nearby tower casts a shadow that is 46.25 m long. How y'all is the tower?

Answer 1

Answer:

Therefore the height of the tower is 116.75 m.

Step-by-step explanation:

Given that a pole that is 2.6 m tall casts a shadow that is 1.03 m long.

Here the height of a object directly proportional to the shadow. It means

Height of the object ∝ shadow

Height of the object= k.shadow

[k is the proportional constant.]

$\Rightarrow \frac{h}{s} =k$    [Height of object is denoted by h and shadow is denoted by s]

Then,

$\frac{h_1}{s_1} =k$       [h₁ is the height of the pole and s₁is the length of the shadow]

Again for the tower

$\frac{h_2}{s_2}=k$      [h₂ is the height of the tower and s₂ is the length of the shadow]

Therefore,

$\frac{h_1}{s_1}=\frac{h_2}{s_2} =k$

$\Rightarrow\frac{h_1}{s_1}=\frac{h_2}{s_2}$............(1)

Given $h_1 = 2.6 m$  ,$s_1=1.03m$  and   $s_2=46.25m$

Putting the value of $h_1,s_1$ and $s_2$  equation (1)

$\frac{2.6}{1.03}=\frac{h_2}{46.25}$

$\Rightarrow h_2 \times1.03= 2.6\times 46.25$          [cross multiplication]

$\Rightarrow h_2 = \frac{2.6\times 46.25}{1.03}$

$\Rightarrow h_2= 116.75$

Therefore the height of the tower is 116.75 m.