Triangle calculator SSS - result

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Obtuse scalene triangle.

Sides: a = 3.16   b = 13.6   c = 12.04

Area: T = 17.48109647331
Perimeter: p = 28.8
Semiperimeter: s = 14.4

Angle ∠ A = α = 12.32884665067° = 12°19'42″ = 0.21551723323 rad
Angle ∠ B = β = 113.2330033508° = 113°13'48″ = 1.97662368969 rad
Angle ∠ C = γ = 54.44114999852° = 54°26'29″ = 0.95501834245 rad

Height: ha = 11.06439017298
Height: hb = 2.57107301078
Height: hc = 2.90438147397

Median: ma = 12.74661523606
Median: mb = 5.58987028907
Median: mc = 7.82551134177

Inradius: r = 1.21439558842
Circumradius: R = 7.43999211128

Vertex coordinates: A[12.04; 0] B[0; 0] C[-1.24663787375; 2.90438147397]
Centroid: CG[3.59878737542; 0.96879382466]
Coordinates of the circumscribed circle: U[6.02; 4.30333048318]
Coordinates of the inscribed circle: I[0.8; 1.21439558842]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.6721533493° = 167°40'18″ = 0.21551723323 rad
∠ B' = β' = 66.77699664919° = 66°46'12″ = 1.97662368969 rad
∠ C' = γ' = 125.5598500015° = 125°33'31″ = 0.95501834245 rad

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How did we calculate this triangle?

a = 3.16 ; ; b = 13.6 ; ; c = 12.04 ; ;

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

p = a+b+c = 3.16+13.6+12.04 = 28.8 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 28.8 }{ 2 } = 14.4 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 14.4 * (14.4-3.16)(14.4-13.6)(14.4-12.04) } ; ; T = sqrt{ 305.58 } = 17.48 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 17.48 }{ 3.16 } = 11.06 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 17.48 }{ 13.6 } = 2.57 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 17.48 }{ 12.04 } = 2.9 ; ;

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{ 13.6**2+12.04**2-3.16**2 }{ 2 * 13.6 * 12.04 } ) = 12° 19'42" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 3.16**2+12.04**2-13.6**2 }{ 2 * 3.16 * 12.04 } ) = 113° 13'48" ; ; gamma = 180° - alpha - beta = 180° - 12° 19'42" - 113° 13'48" = 54° 26'29" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 17.48 }{ 14.4 } = 1.21 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 3.16 }{ 2 * sin 12° 19'42" } = 7.4 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 13.6**2+2 * 12.04**2 - 3.16**2 } }{ 2 } = 12.746 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.04**2+2 * 3.16**2 - 13.6**2 } }{ 2 } = 5.589 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 13.6**2+2 * 3.16**2 - 12.04**2 } }{ 2 } = 7.825 ; ;
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