SOLUTION: Jan observed that the lamp post in front of her house casts a shadow of length 8 feet when the angle of the inclination of the sun in 60 egrees. How tall is the lamp post? (In a 30

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Question 59747: Jan observed that the lamp post in front of her house casts a shadow of length 8 feet when the angle of the inclination of the sun in 60 egrees. How tall is the lamp post? (In a 30-60-90 right angle, the side of the opposite 30 is one-half the length of the hypotenuse)
Answer by uma(370) About Me  (Show Source):
You can put this solution on YOUR website!
The lamp post makes an angle of 90 degrees with the floor.
So the length of the shadow is supposed to be the base of the right triangle and the height of the triangle is represented by the lamp post.
The angle of inclination 60 degrees is the angle made by the hypotenuse of the triangle with the base.
The side opposite the 30 degrees is the base = 8 feet
So hypotenuse = twice the base = 2*8 = 16 feet.
The height of the triangle = sqrt(16^2 - 8^2) [Pythagorean theorem]
= sqrt (256 - 64)
= sqrt(192)
= 13.86 feet (approximately)
The height of the lamp post = 13.86 feet