Triangle calculator SAS

Obtuse scalene triangle.

Sides: a = 736 b = 915 c = 184.084381849

Area: T = 17622.56331861
Perimeter: p = 1835.084381849
Semiperimeter: s = 917.5421909245

Angle ∠ A = α = 12.07883163573° = 12°4'42″ = 0.21108063885 rad
Angle ∠ B = β = 164.9221683643° = 164°55'18″ = 2.87884263875 rad
Angle ∠ C = γ = 3° = 0.05223598776 rad

Height: h_a = 47.88773999623
Height: h_b = 38.51992637948
Height: h_c = 191.4622381981

Median: m_a = 547.8432975783
Median: m_b = 280.1522058916
Median: m_c = 825.2220447482

Inradius: r = 19.20662760388
Circumradius: R = 1758.674445352

Vertex coordinates: A[184.084381849; 0] B[0; 0] C[-710.666036634; 191.4622381981]
Centroid: CG[-175.526551595; 63.82107939938]
Coordinates of the circumscribed circle: U[92.04219092449; 1756.26442513]
Coordinates of the inscribed circle: I[2.54219092449; 19.20662760388]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.9221683643° = 167°55'18″ = 0.21108063885 rad
∠ B' = β' = 15.07883163573° = 15°4'42″ = 2.87884263875 rad
∠ C' = γ' = 177° = 0.05223598776 rad

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How did we calculate this triangle?

1. Calculation of the third side c of the triangle using a Law of Cosines

$a = 736 ; ; b = 915 ; ; gamma = 3° ; ; ; ; c**2 = a**2+b**2 - 2ab cos gamma ; ; c = sqrt{ a**2+b**2 - 2ab cos gamma } ; ; c = sqrt{ 736**2+915**2 - 2 * 736 * 915 * cos 3° } ; ; c = 184.08 ; ;$

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

$a = 736 ; ; b = 915 ; ; c = 184.08 ; ;$

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

$p = a+b+c = 736+915+184.08 = 1835.08 ; ;$

3. Semiperimeter of the triangle

$s = fraction{ o }{ 2 } = fraction{ 1835.08 }{ 2 } = 917.54 ; ;$

4. The triangle area using Heron's formula

$T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 917.54 * (917.54-736)(917.54-915)(917.54-184.08) } ; ; T = sqrt{ 310554733.25 } = 17622.56 ; ;$

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

$T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 17622.56 }{ 736 } = 47.89 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 17622.56 }{ 915 } = 38.52 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 17622.56 }{ 184.08 } = 191.46 ; ;$

6. Calculation of the inner angles of the triangle using a Law of Cosines

$a**2 = b**2+c**2 - 2bc cos alpha ; ; alpha = arccos( fraction{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 915**2+184.08**2-736**2 }{ 2 * 915 * 184.08 } ) = 12° 4'42" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 736**2+184.08**2-915**2 }{ 2 * 736 * 184.08 } ) = 164° 55'18" ; ; gamma = 180° - alpha - beta = 180° - 12° 4'42" - 164° 55'18" = 3° ; ;$

7. Inradius

$T = rs ; ; r = fraction{ T }{ s } = fraction{ 17622.56 }{ 917.54 } = 19.21 ; ;$

8. Circumradius

$R = fraction{ a }{ 2 * sin alpha } = fraction{ 736 }{ 2 * sin 12° 4'42" } = 1758.67 ; ;$

9. Calculation of medians

$m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 915**2+2 * 184.08**2 - 736**2 } }{ 2 } = 547.843 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 184.08**2+2 * 736**2 - 915**2 } }{ 2 } = 280.152 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 915**2+2 * 736**2 - 184.08**2 } }{ 2 } = 825.22 ; ;$
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