Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 14.42   b = 16.12   c = 7.21

Area: T = 51.98440973735
Perimeter: p = 37.75
Semiperimeter: s = 18.875

Angle ∠ A = α = 63.45495203235° = 63°26'58″ = 1.10774030385 rad
Angle ∠ B = β = 89.98217864929° = 89°58'54″ = 1.57704784411 rad
Angle ∠ C = γ = 26.56986931836° = 26°34'7″ = 0.4643711174 rad

Height: ha = 7.21099996357
Height: hb = 6.45496398726
Height: hc = 14.42199992714

Median: ma = 10.19548589985
Median: mb = 8.06220499874
Median: mc = 14.8632683977

Inradius: r = 2.75441243642
Circumradius: R = 8.06600004072

Vertex coordinates: A[7.21; 0] B[0; 0] C[0.00545839112; 14.42199992714]
Centroid: CG[2.40548613037; 4.80766664238]
Coordinates of the circumscribed circle: U[3.605; 7.20988543864]
Coordinates of the inscribed circle: I[2.755; 2.75441243642]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 116.5550479677° = 116°33'2″ = 1.10774030385 rad
∠ B' = β' = 90.01882135071° = 90°1'6″ = 1.57704784411 rad
∠ C' = γ' = 153.4311306816° = 153°25'53″ = 0.4643711174 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 = 14.42+16.12+7.21 = 37.75 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 37.75 }{ 2 } = 18.88 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18.88 * (18.88-14.42)(18.88-16.12)(18.88-7.21) } ; ; T = sqrt{ 2702.35 } = 51.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 51.98 }{ 14.42 } = 7.21 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 51.98 }{ 16.12 } = 6.45 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 51.98 }{ 7.21 } = 14.42 ; ;

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{ 16.12**2+7.21**2-14.42**2 }{ 2 * 16.12 * 7.21 } ) = 63° 26'58" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 14.42**2+7.21**2-16.12**2 }{ 2 * 14.42 * 7.21 } ) = 89° 58'54" ; ; gamma = 180° - alpha - beta = 180° - 63° 26'58" - 89° 58'54" = 26° 34'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 51.98 }{ 18.88 } = 2.75 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 14.42 }{ 2 * sin 63° 26'58" } = 8.06 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 16.12**2+2 * 7.21**2 - 14.42**2 } }{ 2 } = 10.195 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.21**2+2 * 14.42**2 - 16.12**2 } }{ 2 } = 8.062 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 16.12**2+2 * 14.42**2 - 7.21**2 } }{ 2 } = 14.863 ; ;
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