Question

The height of a tower is 100 m. When the angle of elevation of the sun changes from 30° to 45°, the shadow of the tower becomes x metres less. The value of x is
A. 100 m
B. 100√3m
C. 100(√3-1)m
D.100/√3m

Answer 1

The value of x is 100 ( √3 - 1 ) meters  .

Step-by-step explanation:

The height of tower OC = h = 100 meters

The angle of elevation of the sun changes from 30° to 45°

The distance of shadow for elevation of 30° = OB = y meters

The distance of shadow for elevation of 45° = OA = (y - x) meters

According to question

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

i.e Tan 45° = $\dfrac{OC}{OA}$

Or, 1 = $\dfrac{h}{(y-x)}$

i.e  h = y - x              

Or,  y - x  = 100           ........1

Again

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

i.e Tan 30° = $\dfrac{OC}{OB}$

Or, $\dfrac{1}{\sqrt{3} }$ = $\dfrac{h}{y}$

i.e  y = h√3          

Or,  y = 100 √3             ....2

From eq 1 and 2

Put the value of y in eq 1

∵  y - x = 100

Or,  x = y - 100

i.e   x =  100 √3 - 100

∴    x = 100 ( √3 - 1 ) meters

So, The value of x = 100 ( √3 - 1 ) meters

Hence, The value of x is 100 ( √3 - 1 ) meters  . Answer