Question

A 5 m 60 cm high vertical pole casts a shadow
3 m 20 cm long. Find at the same time :
(i) the length of the shadow cast by another
pole 10 m 50 cm high.
(ii) the height of a pole which casts a shadow
5 m long.
Solution :​

Answer 1

Answer:

(i) The length of shadow cast by other pole is 6 meters

(ii)  The height of pole is 8.75 meters .

Step-by-step explanation:

Given as :

The height of the pole = h = 5 m + 60 cm = 5.6 cm

The length of shadow = x = 3 m + 20 cm = 3.2 cm

So, Tan angle = $\dfrac{perpendicular}{base}$

Or, Tan angle = $\dfrac{h}{x}$

Or, Tan angle = $\dfrac{5.6}{3.2}$

i.e Tan angle = $\dfrac{7}{4}$             ......1

Again

(i) At the same time

Let The length of shadow cast by other pole = y            

The height of pole = h' = 10 m 50 cm = 10.5 m

∵ Tan angle = $\dfrac{perpendicular}{base}$

Or, Tan angle = $\dfrac{h'}{y}$

Or, Tan angle = $\dfrac{10.5}{y}$

From eq 1

$\dfrac{7}{4}$  =  $\dfrac{10.5}{y}$

Or, 7 y = 10.5 × 4

∴  y = $\dfrac{10.5\times 4}{7}$

i.e y = 6 m

So, The length of shadow cast by other pole = y = 6 m

Hence, The length of shadow cast by other pole is 6 meters . Answer

Again

At The same time

(ii) The length of pole = z = 5 m

let The height of pole = h"

∵ Tan angle = $\dfrac{perpendicular}{base}$

Or, Tan angle = $\dfrac{h''}{z}$

Or, Tan angle = $\dfrac{h"}{5}$

From eq 1

$\dfrac{7}{4}$  =  $\dfrac{h''}{5}$

Or, h" = $\dfrac{7\times 5}{4}$

∴  h" = 8.75 m

So, The height of pole = h" = 8.75 m

Hence, The height of pole is 8.75 meters . Answer