Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 13.1   b = 8.7   c = 5.53

Area: T = 17.65990545033
Perimeter: p = 27.33
Semiperimeter: s = 13.665

Angle ∠ A = α = 132.7699086939° = 132°46'9″ = 2.3177257712 rad
Angle ∠ B = β = 29.17883402617° = 29°10'42″ = 0.50992581078 rad
Angle ∠ C = γ = 18.05325727993° = 18°3'9″ = 0.31550768338 rad

Height: ha = 2.69660388555
Height: hb = 4.06595527594
Height: hc = 6.38766381567

Median: ma = 3.19988982478
Median: mb = 9.06549296743
Median: mc = 10.77105512858

Inradius: r = 1.29222835348
Circumradius: R = 8.92325346108

Vertex coordinates: A[5.53; 0] B[0; 0] C[11.43876943942; 6.38766381567]
Centroid: CG[5.65658981314; 2.12988793856]
Coordinates of the circumscribed circle: U[2.765; 8.48333011783]
Coordinates of the inscribed circle: I[4.965; 1.29222835348]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 47.23109130611° = 47°13'51″ = 2.3177257712 rad
∠ B' = β' = 150.8221659738° = 150°49'18″ = 0.50992581078 rad
∠ C' = γ' = 161.9477427201° = 161°56'51″ = 0.31550768338 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 = 13.1+8.7+5.53 = 27.33 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 27.33 }{ 2 } = 13.67 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13.67 * (13.67-13.1)(13.67-8.7)(13.67-5.53) } ; ; T = sqrt{ 311.84 } = 17.66 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 17.66 }{ 13.1 } = 2.7 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 17.66 }{ 8.7 } = 4.06 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 17.66 }{ 5.53 } = 6.39 ; ;

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{ 8.7**2+5.53**2-13.1**2 }{ 2 * 8.7 * 5.53 } ) = 132° 46'9" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 13.1**2+5.53**2-8.7**2 }{ 2 * 13.1 * 5.53 } ) = 29° 10'42" ; ;
 gamma = 180° - alpha - beta = 180° - 132° 46'9" - 29° 10'42" = 18° 3'9" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 17.66 }{ 13.67 } = 1.29 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 13.1 }{ 2 * sin 132° 46'9" } = 8.92 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.7**2+2 * 5.53**2 - 13.1**2 } }{ 2 } = 3.199 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.53**2+2 * 13.1**2 - 8.7**2 } }{ 2 } = 9.065 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.7**2+2 * 13.1**2 - 5.53**2 } }{ 2 } = 10.771 ; ;
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