shadow of a tower of height (1+√3)m standing on the ground is found to be x metre at a certain movement and it is 2m longer when the sun's elevation is 30degree. find the sun's elevation when the length of shadow was x metre

Now, case 2 when the shadow is (x+2) metre long

now tan30degree = Height of tower/ Length of shadow in case 2

1/(root3)=(1+root3) / (x+2)

(x+2)=(root3)(1+root3)

(x+2)= root3 + 3

x = root3 + 3 - 2

x = root3 +1 --eq(1)

Now Case 1 when the shadow is x m long

tan theta = height of tower/length of shadow in case1

tan theta = (1+root3)/x

tan theta = (1+root3)/(1+root3) by eq(1)

tan theta = 1

now since tan 45degree =1

therefore the sun's elevation when the shadow is x m long is 45 degrees