Triangle calculator SAS

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


Obtuse scalene triangle.

Sides: a = 90   b = 60.5   c = 63.71770083485

Area: T = 1925.098821178
Perimeter: p = 214.2177008349
Semiperimeter: s = 107.1098504174

Angle ∠ A = α = 92.82443525067° = 92°49'28″ = 1.62200905773 rad
Angle ∠ B = β = 42.17656474933° = 42°10'32″ = 0.73661039129 rad
Angle ∠ C = γ = 45° = 0.78553981634 rad

Height: ha = 42.78799602618
Height: hb = 63.64396103068
Height: hc = 60.42765097084

Median: ma = 42.83875253305
Median: mb = 71.86770026955
Median: mc = 69.75107040235

Inradius: r = 17.97333460627
Circumradius: R = 45.05547286801

Vertex coordinates: A[63.71770083485; 0] B[0; 0] C[66.6988102855; 60.42765097084]
Centroid: CG[43.47217037345; 20.14221699028]
Coordinates of the circumscribed circle: U[31.85985041742; 31.85985041742]
Coordinates of the inscribed circle: I[46.60985041742; 17.97333460627]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 87.17656474933° = 87°10'32″ = 1.62200905773 rad
∠ B' = β' = 137.8244352507° = 137°49'28″ = 0.73661039129 rad
∠ C' = γ' = 135° = 0.78553981634 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 = 90 ; ; b = 60.5 ; ; gamma = 45° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 90**2+60.5**2 - 2 * 90 * 60.5 * cos(45° ) } ; ; c = 63.72 ; ;


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 = 90 ; ; b = 60.5 ; ; c = 63.72 ; ;

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

p = a+b+c = 90+60.5+63.72 = 214.22 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 214.22 }{ 2 } = 107.11 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 107.11 * (107.11-90)(107.11-60.5)(107.11-63.72) } ; ; T = sqrt{ 3706003.13 } = 1925.1 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1925.1 }{ 90 } = 42.78 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1925.1 }{ 60.5 } = 63.64 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1925.1 }{ 63.72 } = 60.43 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 90**2-60.5**2-63.72**2 }{ 2 * 60.5 * 63.72 } ) = 92° 49'28" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 60.5**2-90**2-63.72**2 }{ 2 * 90 * 63.72 } ) = 42° 10'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 63.72**2-90**2-60.5**2 }{ 2 * 60.5 * 90 } ) = 45° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1925.1 }{ 107.11 } = 17.97 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 90 }{ 2 * sin 92° 49'28" } = 45.05 ; ;




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