Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 17   b = 23   c = 30

Area: T = 194.4222220952
Perimeter: p = 70
Semiperimeter: s = 35

Angle ∠ A = α = 34.30111527568° = 34°18'4″ = 0.59986680528 rad
Angle ∠ B = β = 49.687978493° = 49°40'47″ = 0.86770758187 rad
Angle ∠ C = γ = 96.01990623132° = 96°1'9″ = 1.6765848782 rad

Height: ha = 22.8733202465
Height: hb = 16.90662800828
Height: hc = 12.96114813968

Median: ma = 25.34326517949
Median: mb = 21.5
Median: mc = 13.56546599663

Inradius: r = 5.55549205986
Circumradius: R = 15.08331524588

Vertex coordinates: A[30; 0] B[0; 0] C[11; 12.96114813968]
Centroid: CG[13.66766666667; 4.32204937989]
Coordinates of the circumscribed circle: U[15; -1.58216093371]
Coordinates of the inscribed circle: I[12; 5.55549205986]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.6998847243° = 145°41'56″ = 0.59986680528 rad
∠ B' = β' = 130.322021507° = 130°19'13″ = 0.86770758187 rad
∠ C' = γ' = 83.98109376868° = 83°58'51″ = 1.6765848782 rad

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How did we calculate this triangle?

a = 17 ; ; b = 23 ; ; c = 30 ; ;

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

p = a+b+c = 17+23+30 = 70 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 70 }{ 2 } = 35 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35 * (35-17)(35-23)(35-30) } ; ; T = sqrt{ 37800 } = 194.42 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 194.42 }{ 17 } = 22.87 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 194.42 }{ 23 } = 16.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 194.42 }{ 30 } = 12.96 ; ;

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{ 17**2-23**2-30**2 }{ 2 * 23 * 30 } ) = 34° 18'4" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-17**2-30**2 }{ 2 * 17 * 30 } ) = 49° 40'47" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-17**2-23**2 }{ 2 * 23 * 17 } ) = 96° 1'9" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 194.42 }{ 35 } = 5.55 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 34° 18'4" } = 15.08 ; ;

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