SOLUTION: Find the perimeter of the equilateral traiangle inscribed in a circle of radius 20.0 inches

Question 168637: Find the perimeter of the equilateral traiangle inscribed in a circle of radius 20.0 inches
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!

AC is equal to the radius 20.
We know that angle C is half of the original angle of the original equilateral triangle(60) ....so C is 60/2=30. ABC is a right triangle so we know that angle A is a 60 degree angle 180-90-30=60
:
BC is equal to 1/2 of the entire side of the equilateral triangle
and we know that sine 60 degrees =BC/20(hypothenuse of the ABC)--->solving for BC=20(sine60degrees)=17.32
:
now if we double BC we will have the entire length of one side of the equilateral triangle ( 17.32(2)=34.64)---> and since all sides are equal the Perimeter is three times this length. 34.64(3)=103.92 inches
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