Triangle calculator SAS

Please enter two sides of the triangle and the included angle
°


Obtuse scalene triangle.

Sides: a = 0.445   b = 90   c = 89.55550333755

Area: T = 0.24546454416
Perimeter: p = 1800.000033376
Semiperimeter: s = 900.0000166878

Angle ∠ A = α = 0.00334782217° = 0°13″ = 06.07064E-5 rad
Angle ∠ B = β = 179.2976521778° = 179°17'47″ = 3.12993146424 rad
Angle ∠ C = γ = 0.7° = 0°42' = 0.01222173048 rad

Height: ha = 1.10995300748
Height: hb = 0.00554365654
Height: hc = 0.00554635777

Median: ma = 89.77875166464
Median: mb = 44.55550335422
Median: mc = 45.22224834764

Inradius: r = 0.00327182822
Circumradius: R = 3665.181072209

Vertex coordinates: A[89.55550333755; 0] B[0; 0] C[-0.44549664586; 0.00554635777]
Centroid: CG[29.7033355639; 0.00218211926]
Coordinates of the circumscribed circle: U[44.77875166878; 3664.907724939]
Coordinates of the inscribed circle: I[01.66878E-5; 0.00327182822]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 179.9976521778° = 179°59'47″ = 06.07064E-5 rad
∠ B' = β' = 0.70334782216° = 0°42'13″ = 3.12993146424 rad
∠ C' = γ' = 179.3° = 179°18' = 0.01222173048 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 = 0.45 ; ; b = 90 ; ; gamma = 0° 42' ; ; ; ; c**2 = a**2+b**2 - 2ab cos gamma ; ; c = sqrt{ a**2+b**2 - 2ab cos gamma } ; ; c = sqrt{ 0.45**2+90**2 - 2 * 0.45 * 90 * cos 0° 42' } ; ; c = 89.56 ; ;
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 = 0.45 ; ; b = 90 ; ; c = 89.56 ; ;

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

p = a+b+c = 0.45+90+89.56 = 180 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 180 }{ 2 } = 90 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 90 * (90-0.45)(90-90)(90-89.56) } ; ; T = sqrt{ 0.06 } = 0.24 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.24 }{ 0.45 } = 1.1 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.24 }{ 90 } = 0.01 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.24 }{ 89.56 } = 0.01 ; ;

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{ 90**2+89.56**2-0.45**2 }{ 2 * 90 * 89.56 } ) = 0° 13" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 0.45**2+89.56**2-90**2 }{ 2 * 0.45 * 89.56 } ) = 179° 17'47" ; ; gamma = 180° - alpha - beta = 180° - 0° 13" - 179° 17'47" = 0° 42' ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.24 }{ 90 } = 0 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 0.45 }{ 2 * sin 0° 13" } = 3665.18 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 89.56**2 - 0.45**2 } }{ 2 } = 89.778 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 89.56**2+2 * 0.45**2 - 90**2 } }{ 2 } = 44.555 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 0.45**2 - 89.56**2 } }{ 2 } = 45.222 ; ;
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