Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 17   b = 19   c = 28

Area: T = 157.9877341265
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 36.43769168605° = 36°26'13″ = 0.63659441685 rad
Angle ∠ B = β = 41.59112771434° = 41°35'29″ = 0.72659047263 rad
Angle ∠ C = γ = 101.9721805996° = 101°58'19″ = 1.78797437588 rad

Height: ha = 18.58767460312
Height: hb = 16.6330246449
Height: hc = 11.28548100904

Median: ma = 22.36662692463
Median: mb = 21.12546301743
Median: mc = 11.35878166916

Inradius: r = 4.93771044145
Circumradius: R = 14.31112731811

Vertex coordinates: A[28; 0] B[0; 0] C[12.71442857143; 11.28548100904]
Centroid: CG[13.57114285714; 3.76216033635]
Coordinates of the circumscribed circle: U[14; -2.96985922698]
Coordinates of the inscribed circle: I[13; 4.93771044145]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.5633083139° = 143°33'47″ = 0.63659441685 rad
∠ B' = β' = 138.4098722857° = 138°24'31″ = 0.72659047263 rad
∠ C' = γ' = 78.02881940039° = 78°1'41″ = 1.78797437588 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 = 17+19+28 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-17)(32-19)(32-28) } ; ; T = sqrt{ 24960 } = 157.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 157.99 }{ 17 } = 18.59 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 157.99 }{ 19 } = 16.63 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 157.99 }{ 28 } = 11.28 ; ;

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{ 19**2+28**2-17**2 }{ 2 * 19 * 28 } ) = 36° 26'13" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 17**2+28**2-19**2 }{ 2 * 17 * 28 } ) = 41° 35'29" ; ; gamma = 180° - alpha - beta = 180° - 36° 26'13" - 41° 35'29" = 101° 58'19" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 157.99 }{ 32 } = 4.94 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 17 }{ 2 * sin 36° 26'13" } = 14.31 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 19**2+2 * 28**2 - 17**2 } }{ 2 } = 22.366 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 17**2 - 19**2 } }{ 2 } = 21.125 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 19**2+2 * 17**2 - 28**2 } }{ 2 } = 11.358 ; ;
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