SOLUTION: Kari has an analog clock, shown here, with a minute hand of length 12 in. When Kari’s clock strikes 2 o’clock, what is the area of the right triangle formed by drawing a segment fr

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Question 457874: Kari has an analog clock, shown here, with a minute hand of length 12 in. When Kari’s clock strikes 2 o’clock, what is the area of the right triangle formed by drawing a segment from the end of the minute hand to the end of the hour hand? Express your answer in simplest radical form.
Answer by Edwin McCravy(20056) About Me  (Show Source):
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Kari has an analog clock, shown here, with a minute hand of length 12 in. When Kari’s clock strikes 2 o’clock, what is the area of the right triangle formed by drawing a segment from the end of the minute hand to the end of the hour hand? Express your answer in simplest radical form.
The angle between the hands at 2:00 is 2/12ths of 360°
or 1/6th of 360° or 60° 





Therefore the triangle is a 60°-30°-90° right triangle.  The hypotenuse
of such a right triangle is twice the shorter leg.  Therefore
the shorter leg is half of 12 in. or 6 in.

The green line is found by the Pythagorean theorem.

 c˛ = a˛ + b˛
12˛ = 6˛ + b˛
144 = 36 + b˛
108 = b˛
 b˛ = 108
       ___
  b = √108
       ____
  b = √36*3
        _
  b = 6√3


The formula for the area of a triangle is

   A = ˝(base)(height)
                     _
base = 6, height = 6√3
              _
   A = ˝(6)(6√3)
          _
   A = 18√3 square feet.

Edwin