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Question 62051: betty observed that the lamp post in front of her house cast a shadow of length 8 feet when the angle of inclination of the sun is 60 degrees. How tall is the lamp post? (In a 30-60-90 right triangle, the side opposite 30 is 1/2 the length of the hypotenuse.
Answer by dolly(163)   (Show Source):
You can put this solution on YOUR website! 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.
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