Question

The length of the shadow of a tower when the size of the sun's angles is 30° is 21m more than the the length of the time it is 45 , then prove that the height of tower is x ( √3 + 1 ) ​

Answer 1

Step-by-step explanation:

Step 1:

Given Data:

Length of a tower is 2x

To prove the height of the tower is x(root 3 +1) metre

Step 2:

In angle BCD,

tan 45=h/y

h=y………..(1)

Step 3:

In angle ABC,

Tan 30=h/(2x+y)

Step 4:

i/ √3 =h/2x+y

2x+y= √3h

Step 5:

Substitute y=h from equation (1)

2x+h= √3h

2x= (√3-1)h

Step 6:

\mathrm{h}=\frac{2 \mathrm{x}}{\sqrt{3}-1} \times \frac{\sqrt{3}+1}{\sqrt{3}+1}h=

3

−1

2x

×

3

+1

3

+1

h=(√3+1)x

Hence it is proved