Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 14   b = 15   c = 23

Area: T = 101.4699207152
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 36.03113118284° = 36°1'53″ = 0.62988650252 rad
Angle ∠ B = β = 39.06880914837° = 39°4'5″ = 0.68218668289 rad
Angle ∠ C = γ = 104.9010596688° = 104°54'2″ = 1.83108607995 rad

Height: ha = 14.49656010217
Height: hb = 13.52992276202
Height: hc = 8.82334093175

Median: ma = 18.11107702763
Median: mb = 17.5
Median: mc = 8.84659030065

Inradius: r = 3.90326618135
Circumradius: R = 11.99001619693

Vertex coordinates: A[23; 0] B[0; 0] C[10.87695652174; 8.82334093175]
Centroid: CG[11.29898550725; 2.94111364392]
Coordinates of the circumscribed circle: U[11.5; -3.06600416492]
Coordinates of the inscribed circle: I[11; 3.90326618135]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.9698688172° = 143°58'7″ = 0.62988650252 rad
∠ B' = β' = 140.9321908516° = 140°55'55″ = 0.68218668289 rad
∠ C' = γ' = 75.09994033122° = 75°5'58″ = 1.83108607995 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+15+23 = 52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 52 }{ 2 } = 26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26 * (26-14)(26-15)(26-23) } ; ; T = sqrt{ 10296 } = 101.47 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 101.47 }{ 14 } = 14.5 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 101.47 }{ 15 } = 13.53 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 101.47 }{ 23 } = 8.82 ; ;

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{ 15**2+23**2-14**2 }{ 2 * 15 * 23 } ) = 36° 1'53" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 14**2+23**2-15**2 }{ 2 * 14 * 23 } ) = 39° 4'5" ; ; gamma = 180° - alpha - beta = 180° - 36° 1'53" - 39° 4'5" = 104° 54'2" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 101.47 }{ 26 } = 3.9 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 14 }{ 2 * sin 36° 1'53" } = 11.9 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 15**2+2 * 23**2 - 14**2 } }{ 2 } = 18.111 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 14**2 - 15**2 } }{ 2 } = 17.5 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 15**2+2 * 14**2 - 23**2 } }{ 2 } = 8.846 ; ;
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