SOLUTION: Find the circumference of a circle inscribed in an equilateral triangle if the height of the triangle is 14 in.

Question 113324: Find the circumference of a circle inscribed in an equilateral triangle if the height of the triangle is 14 in.
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
THIS EQUILATERAL TRIANGLE WITH A HEIGHT OF 14 IN. HAS SIDES OF:
14/SQRT3=X/2 (THIS IS HALF OF THE TRIANGLE FORMED BY THE HEIGHT, 1 SIDE & HALF THE BASE)
SQRT3*X=28
X=28/SQRT3
X=16.66 IN. FOR THE LENGTH OF THE SIDES.
NOW DISECT ONE OF THE LOWER ANGLES FORMINGA 30-6-90 DEGREE TRIANGLE WITH ONE HALF THE SIDE(8.083 IN)OPPOSITE THE 60 DEGREE ANGLE.
THEREFORE THE OTHER SIDE IS:
X/1=8.083/SQRT3
X=8.083/1.732
X=4.667 IN FOR THE RADIUS.
THUS THE CIRCUMFERANCE OF THE INSCRIBED CIRCLE IS 2*PI*4.667=29.3 INCHES.

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