Question 62051
The scenario picturizes a right triangle.

The length of the shadow = base of the triangle = 8 feet.

angle of inclination = 60 degrees.

Height of the lamp post = height of the triangle.

The side opposite to 30 degrees is the base of the triangle = 8ft.

Given this is half the hypotenuse.

That is hypotenuse = 2* 8 

                   = 16 ft.

By Pythagorean theorem,

The height = sqrt [(hypo)^2 - (base)^2 ]

==> ht = sqrt [ 16^2 - 8^2]

==>    = sqrt [256 - 64]
==>    = sqrt [ 192 ]

==>    = sqrt [ 64*3]

==>    = sqrt [64] * sqrt(3)

==>    = 8 * 1.732

==>    = 13.856

The ht of the lamp post = 13.86 ft.