Question 58585
Betty observed that the lamppost in the front of her house cases a shadow of length 8 feet when the angle of inclination of the sun is 60 degrees. How tall is the lamppost? (In a 30-60-90 right triangle, the side opposite 30 is one-half the length of the hypotenuse) 
not sure how to solve 
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Draw the picture.
You should see a right triangle with the right
angle at the base of the pole and the 60 degree
angle opposite the pole at ground-level.
The distance from the vertex of the 60 degree
angle to the base of the pole is the shadow
which is 8 ft long.
The angle at the top of the pole is 30 degrees
and the shadow is the side opposite the 30 degree
angle.
So, sine the side opposite the 30 degree angle
is one-half the hypotenuse, the hypotenuse must
be 16 ft.
Now, using Pythagoras: hypotenuse^2 = 8^2 + pole^2
16^2 = 8^2 + pole^2
256 = 64 + pole^2
pole^2 = 192
pole^2 = 64*3
pole = 8sqrt(3)
Cheers,
Stan H.