Question 1143114
Use Heron's formula for the area of a triangle given the length of all three sides
:
s = (a + b + c)/2 = (12 + 15 + 18)/2 = 45/2 = 22.5
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Area(A) = square root(22.5 * (22.5-12) * (22.5-15) * (22.5-18)) = 89.29 square inches
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A = r * s, where r is the radius of the inscribed circle
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r = A/s = 89.29/22.5 = 3.97 inches
:
let a = 12, b = 15, c = 18, use law of cosines to find angle A
:
12^2 = 15^2 +18^2 - 2 * 15 * 18 * cos(A)
:
cos(A) = (15^2 +18^2 -12^2)/(2 * 15 * 18) = 0.75
:
Angle A = cos^-1 (0.75) = 41.41 degrees
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Use the law of sines, where R is the radius of the circumscribed circle
:
R = a/(2 * sin A) = 12/(2 * sin (41.41) = 9.07 inches
:
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Area of triangle is 89.29 square inches
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radius of inscribed circle is 3.97 inches
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radius of circumscribed circle is 9.07 inches
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