Thread: Equilateral Triangle
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Old November 20th, 2008, 08:31 AM
Soroban Soroban is offline
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Hello, magentarita!

Quote:
Find the perimeter of the equilateral triangle inscribed in a circle of radius 20 inches
Code:
                A
              * * *
          *    /|\    *
        *     / | \     *
       *     /  |  \     *
            / 20|   \  D
      *    /    |    *    *
      *   /     *     \   *
      *  /      O      \  *
        /               \
     B *- - - - - - - - -* C
        *               *
          *           *
              * * *

The triangle is ABC
The circle has center O and radius OA = 20
Draw OD \perp AC.

Since \Delta ABC is equilateral, \angle A \:=\:\angle B \:=\:\angle C \:=\:60^o
. . Then: \angle OAD = 30^o

In right triangle ADO\!:\;\;\cos30^o \:=\:\frac{AD}{20} \quad\Rightarrow\quad AD \:=\:20\cos30^o \:\approx\:17.32 inches

The side of the triangle is: .2\times 17.32 \:=\:34.64 inches


Therefore, the perimeter is: .3 \times 34.64 \:=\:103.92 inches.
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