Height of a post. Betty observed that the lamppost in the front of her house
cases a show 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 

                |
              - O -
                |


                       
          |
        --o--
         /|
        / | 
     h /  | 
      /30°|x
     /    | 
    /     | 
   /60°   |
   ¯¯¯¯¯¯¯
     8 ft

Let x be the height of the lamp post. I have marked
the hypotenuse h. The shadow is the line marked 8 ft. 
It is the side opposite the 30° angle. Therefore 

h = 2 × 8 ft or 16 ft. 

I will now re-draw the picture putting
16 ft. where the h is:

                |
              - O -
                |


                       
          |
        --o--
         /|
        / | 
    16 /  | 
      /30°|x
     /    | 
    /     | 
   /60°   |
   ¯¯¯¯¯¯¯
     8 ft


Now we can use the Pythagorean theorem

       c² = a² + b²

where c = 16, a = 8, and b = x. Substitute these

       c² = a² + b²
    (16)² = (8)² + x²
      256 = 64 + x²

Subtract 64 from both sides

      192 = x²

Take square root of both sides:
      ___
     Ö192 = x
     13.9 = x

The lampost is approximately 13.9 ft tall.

Edwin