Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 13   b = 15   c = 26

Area: T = 67.35498329619
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 20.20552235834° = 20°12'19″ = 0.35326476776 rad
Angle ∠ B = β = 23.48656716959° = 23°29'8″ = 0.41099022981 rad
Angle ∠ C = γ = 136.3099104721° = 136°18'33″ = 2.37990426778 rad

Height: ha = 10.36215127634
Height: hb = 8.98799777283
Height: hc = 5.18107563817

Median: ma = 20.20551973512
Median: mb = 19.1387659209
Median: mc = 5.29215026221

Inradius: r = 2.49444382578
Circumradius: R = 18.82196457847

Vertex coordinates: A[26; 0] B[0; 0] C[11.92330769231; 5.18107563817]
Centroid: CG[12.6411025641; 1.72769187939]
Coordinates of the circumscribed circle: U[13; -13.60880515674]
Coordinates of the inscribed circle: I[12; 2.49444382578]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.7954776417° = 159°47'41″ = 0.35326476776 rad
∠ B' = β' = 156.5144328304° = 156°30'52″ = 0.41099022981 rad
∠ C' = γ' = 43.69108952793° = 43°41'27″ = 2.37990426778 rad

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How did we calculate this triangle?

a = 13 ; ; b = 15 ; ; c = 26 ; ;

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

p = a+b+c = 13+15+26 = 54 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 54 }{ 2 } = 27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27 * (27-13)(27-15)(27-26) } ; ; T = sqrt{ 4536 } = 67.35 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 67.35 }{ 13 } = 10.36 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 67.35 }{ 15 } = 8.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 67.35 }{ 26 } = 5.18 ; ;

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{ 13**2-15**2-26**2 }{ 2 * 15 * 26 } ) = 20° 12'19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-13**2-26**2 }{ 2 * 13 * 26 } ) = 23° 29'8" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-13**2-15**2 }{ 2 * 15 * 13 } ) = 136° 18'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 67.35 }{ 27 } = 2.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 20° 12'19" } = 18.82 ; ;

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