Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 8.1   b = 10.6   c = 15.25

Area: T = 40.70327466393
Perimeter: p = 33.95
Semiperimeter: s = 16.975

Angle ∠ A = α = 30.23878677315° = 30°14'16″ = 0.52877503507 rad
Angle ∠ B = β = 41.22552046495° = 41°13'31″ = 0.72195155559 rad
Angle ∠ C = γ = 108.5376927619° = 108°32'13″ = 1.8944326747 rad

Height: ha = 10.05500608986
Height: hb = 7.68797635169
Height: hc = 5.3388065133

Median: ma = 12.49223476577
Median: mb = 110.9998295441
Median: mc = 5.55437712412

Inradius: r = 2.39878053985
Circumradius: R = 8.04222398248

Vertex coordinates: A[15.25; 0] B[0; 0] C[6.09222131148; 5.3388065133]
Centroid: CG[7.11440710383; 1.77993550443]
Coordinates of the circumscribed circle: U[7.625; -2.55767550526]
Coordinates of the inscribed circle: I[6.375; 2.39878053985]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.7622132269° = 149°45'44″ = 0.52877503507 rad
∠ B' = β' = 138.7754795351° = 138°46'29″ = 0.72195155559 rad
∠ C' = γ' = 71.4633072381° = 71°27'47″ = 1.8944326747 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 = 8.1+10.6+15.25 = 33.95 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 33.95 }{ 2 } = 16.98 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16.98 * (16.98-8.1)(16.98-10.6)(16.98-15.25) } ; ; T = sqrt{ 1656.71 } = 40.7 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 40.7 }{ 8.1 } = 10.05 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 40.7 }{ 10.6 } = 7.68 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 40.7 }{ 15.25 } = 5.34 ; ;

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{ 10.6**2+15.25**2-8.1**2 }{ 2 * 10.6 * 15.25 } ) = 30° 14'16" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 8.1**2+15.25**2-10.6**2 }{ 2 * 8.1 * 15.25 } ) = 41° 13'31" ; ; gamma = 180° - alpha - beta = 180° - 30° 14'16" - 41° 13'31" = 108° 32'13" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 40.7 }{ 16.98 } = 2.4 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 8.1 }{ 2 * sin 30° 14'16" } = 8.04 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.6**2+2 * 15.25**2 - 8.1**2 } }{ 2 } = 12.492 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 15.25**2+2 * 8.1**2 - 10.6**2 } }{ 2 } = 11 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.6**2+2 * 8.1**2 - 15.25**2 } }{ 2 } = 5.554 ; ;
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