Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 95   b = 125   c = 164.72

Area: T = 5904.977040616
Perimeter: p = 384.72
Semiperimeter: s = 192.36

Angle ∠ A = α = 355.0000067528° = 35° = 0.61108653561 rad
Angle ∠ B = β = 498.9996842138° = 48°59'59″ = 0.8555205822 rad
Angle ∠ C = γ = 966.0003090333° = 96°1″ = 1.67655214756 rad

Height: ha = 124.3155166445
Height: hb = 94.48795264986
Height: hc = 71.6977066612

Median: ma = 138.2844450319
Median: mb = 119.0498684159
Median: mc = 74.44334711711

Inradius: r = 30.6977496393
Circumradius: R = 82.81437088528

Vertex coordinates: A[164.72; 0] B[0; 0] C[62.3266002914; 71.6977066612]
Centroid: CG[75.68220009713; 23.8999022204]
Coordinates of the circumscribed circle: U[82.36; -8.6576833945]
Coordinates of the inscribed circle: I[67.36; 30.6977496393]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 1454.999993247° = 145° = 0.61108653561 rad
∠ B' = β' = 1311.000315786° = 131°1″ = 0.8555205822 rad
∠ C' = γ' = 843.9996909667° = 83°59'59″ = 1.67655214756 rad

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How did we calculate this triangle?

a = 95 ; ; b = 125 ; ; c = 164.72 ; ;

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

p = a+b+c = 95+125+164.72 = 384.72 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 384.72 }{ 2 } = 192.36 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 192.36 * (192.36-95)(192.36-125)(192.36-164.72) } ; ; T = sqrt{ 34868675.5 } = 5904.97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5904.97 }{ 95 } = 124.32 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5904.97 }{ 125 } = 94.48 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5904.97 }{ 164.72 } = 71.7 ; ;

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{ 125**2+164.72**2-95**2 }{ 2 * 125 * 164.72 } ) = 35° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 95**2+164.72**2-125**2 }{ 2 * 95 * 164.72 } ) = 48° 59'59" ; ; gamma = 180° - alpha - beta = 180° - 35° - 48° 59'59" = 96° 1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5904.97 }{ 192.36 } = 30.7 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 95 }{ 2 * sin 35° } = 82.81 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 125**2+2 * 164.72**2 - 95**2 } }{ 2 } = 138.284 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 164.72**2+2 * 95**2 - 125**2 } }{ 2 } = 119.049 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 125**2+2 * 95**2 - 164.72**2 } }{ 2 } = 74.443 ; ;
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