Triangle calculator SSS - result

Please enter the triangle sides:


Right scalene Pythagorean triangle.

Sides: a = 165   b = 220   c = 275

Area: T = 18150
Perimeter: p = 660
Semiperimeter: s = 330

Angle ∠ A = α = 36.87698976458° = 36°52'12″ = 0.64435011088 rad
Angle ∠ B = β = 53.13301023542° = 53°7'48″ = 0.9277295218 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 220
Height: hb = 165
Height: hc = 132

Median: ma = 234.9660102996
Median: mb = 198.305532015
Median: mc = 137.5

Inradius: r = 55
Circumradius: R = 137.5

Vertex coordinates: A[275; 0] B[0; 0] C[99; 132]
Centroid: CG[124.6676666667; 44]
Coordinates of the circumscribed circle: U[137.5; 0]
Coordinates of the inscribed circle: I[110; 55]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.1330102354° = 143°7'48″ = 0.64435011088 rad
∠ B' = β' = 126.8769897646° = 126°52'12″ = 0.9277295218 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

a = 165 ; ; b = 220 ; ; c = 275 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 165+220+275 = 660 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 660 }{ 2 } = 330 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 330 * (330-165)(330-220)(330-275) } ; ; T = sqrt{ 329422500 } = 18150 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 18150 }{ 165 } = 220 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 18150 }{ 220 } = 165 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 18150 }{ 275 } = 132 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 165**2-220**2-275**2 }{ 2 * 220 * 275 } ) = 36° 52'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 220**2-165**2-275**2 }{ 2 * 165 * 275 } ) = 53° 7'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 275**2-165**2-220**2 }{ 2 * 220 * 165 } ) = 90° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 18150 }{ 330 } = 55 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 165 }{ 2 * sin 36° 52'12" } = 137.5 ; ;

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