Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 58.05   b = 16.82   c = 61

Area: T = 487.9021936633
Perimeter: p = 135.87
Semiperimeter: s = 67.935

Angle ∠ A = α = 722.0001565716° = 72°1″ = 1.25766397941 rad
Angle ∠ B = β = 15.99659301832° = 15°59'45″ = 0.27991816486 rad
Angle ∠ C = γ = 92.00439132451° = 92°14″ = 1.60657712108 rad

Height: ha = 16.81097135791
Height: hb = 58.01444990051
Height: hc = 15.99767848076

Median: ma = 34.05215135493
Median: mb = 58.9466358242
Median: mc = 29.93550538667

Inradius: r = 7.18218935252
Circumradius: R = 30.5198663961

Vertex coordinates: A[61; 0] B[0; 0] C[55.80223778689; 15.99767848076]
Centroid: CG[38.93441259563; 5.33222616025]
Coordinates of the circumscribed circle: U[30.5; -1.06771691346]
Coordinates of the inscribed circle: I[51.115; 7.18218935252]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 1087.999843428° = 107°59'59″ = 1.25766397941 rad
∠ B' = β' = 164.0044069817° = 164°15″ = 0.27991816486 rad
∠ C' = γ' = 87.99660867549° = 87°59'46″ = 1.60657712108 rad

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How did we calculate this triangle?

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

p = a+b+c = 58.05+16.82+61 = 135.87 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 135.87 }{ 2 } = 67.94 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 67.94 * (67.94-58.05)(67.94-16.82)(67.94-61) } ; ; T = sqrt{ 238048.3 } = 487.9 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 487.9 }{ 58.05 } = 16.81 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 487.9 }{ 16.82 } = 58.01 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 487.9 }{ 61 } = 16 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 16.82**2+61**2-58.05**2 }{ 2 * 16.82 * 61 } ) = 72° 1" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 58.05**2+61**2-16.82**2 }{ 2 * 58.05 * 61 } ) = 15° 59'45" ; ;
 gamma = 180° - alpha - beta = 180° - 72° 1" - 15° 59'45" = 92° 14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 487.9 }{ 67.94 } = 7.18 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 58.05 }{ 2 * sin 72° 1" } = 30.52 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 16.82**2+2 * 61**2 - 58.05**2 } }{ 2 } = 34.052 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 61**2+2 * 58.05**2 - 16.82**2 } }{ 2 } = 58.946 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 16.82**2+2 * 58.05**2 - 61**2 } }{ 2 } = 29.935 ; ;
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