Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 5.6   b = 3.9   c = 2.18

Area: T = 3.15546664863
Perimeter: p = 11.68
Semiperimeter: s = 5.84

Angle ∠ A = α = 132.0899400414° = 132°5'22″ = 2.30553949442 rad
Angle ∠ B = β = 31.11991534596° = 31°7'9″ = 0.54331316883 rad
Angle ∠ C = γ = 16.79114461263° = 16°47'29″ = 0.29330660211 rad

Height: ha = 1.12766666023
Height: hb = 1.61877776853
Height: hc = 2.8944189437

Median: ma = 1.46332839779
Median: mb = 3.77554072628
Median: mc = 4.70107339852

Inradius: r = 0.54401826175
Circumradius: R = 3.77330771388

Vertex coordinates: A[2.18; 0] B[0; 0] C[4.79441284404; 2.8944189437]
Centroid: CG[2.32547094801; 0.96547298123]
Coordinates of the circumscribed circle: U[1.09; 3.61222030805]
Coordinates of the inscribed circle: I[1.94; 0.54401826175]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 47.91105995858° = 47°54'38″ = 2.30553949442 rad
∠ B' = β' = 148.881084654° = 148°52'51″ = 0.54331316883 rad
∠ C' = γ' = 163.2098553874° = 163°12'31″ = 0.29330660211 rad

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How did we calculate this triangle?

a = 5.6 ; ; b = 3.9 ; ; c = 2.18 ; ;

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

p = a+b+c = 5.6+3.9+2.18 = 11.68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 11.68 }{ 2 } = 5.84 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 5.84 * (5.84-5.6)(5.84-3.9)(5.84-2.18) } ; ; T = sqrt{ 9.95 } = 3.15 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3.15 }{ 5.6 } = 1.13 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3.15 }{ 3.9 } = 1.62 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3.15 }{ 2.18 } = 2.89 ; ;

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{ 3.9**2+2.18**2-5.6**2 }{ 2 * 3.9 * 2.18 } ) = 132° 5'22" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5.6**2+2.18**2-3.9**2 }{ 2 * 5.6 * 2.18 } ) = 31° 7'9" ; ; gamma = 180° - alpha - beta = 180° - 132° 5'22" - 31° 7'9" = 16° 47'29" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3.15 }{ 5.84 } = 0.54 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5.6 }{ 2 * sin 132° 5'22" } = 3.77 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.9**2+2 * 2.18**2 - 5.6**2 } }{ 2 } = 1.463 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.18**2+2 * 5.6**2 - 3.9**2 } }{ 2 } = 3.775 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.9**2+2 * 5.6**2 - 2.18**2 } }{ 2 } = 4.701 ; ;
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