Triangle calculator SAS

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


Obtuse scalene triangle.

Sides: a = 10.1   b = 6.2   c = 6.37990746246

Area: T = 18.93299982863
Perimeter: p = 22.67990746246
Semiperimeter: s = 11.34395373123

Angle ∠ A = α = 106.8111228759° = 106°48'40″ = 1.86442076199 rad
Angle ∠ B = β = 35.98987712412° = 35°59'20″ = 0.62881225519 rad
Angle ∠ C = γ = 37.2° = 37°12' = 0.64992624817 rad

Height: ha = 3.74985145121
Height: hb = 6.10664510601
Height: hc = 5.93550295772

Median: ma = 3.75501728671
Median: mb = 7.85875630149
Median: mc = 7.74993129846

Inradius: r = 1.66993801312
Circumradius: R = 5.27554581241

Vertex coordinates: A[6.37990746246; 0] B[0; 0] C[8.17222349402; 5.93550295772]
Centroid: CG[4.85504365216; 1.97883431924]
Coordinates of the circumscribed circle: U[3.19895373123; 4.20220602271]
Coordinates of the inscribed circle: I[5.14395373123; 1.66993801312]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 73.18987712412° = 73°11'20″ = 1.86442076199 rad
∠ B' = β' = 144.0111228759° = 144°40″ = 0.62881225519 rad
∠ C' = γ' = 142.8° = 142°48' = 0.64992624817 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 = 10.1 ; ; b = 6.2 ; ; gamma = 37° 12' ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 10.1**2+6.2**2 - 2 * 10.1 * 6.2 * cos(37° 12') } ; ; c = 6.38 ; ;


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 = 10.1 ; ; b = 6.2 ; ; c = 6.38 ; ;

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

p = a+b+c = 10.1+6.2+6.38 = 22.68 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 22.68 }{ 2 } = 11.34 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11.34 * (11.34-10.1)(11.34-6.2)(11.34-6.38) } ; ; T = sqrt{ 358.34 } = 18.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 18.93 }{ 10.1 } = 3.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 18.93 }{ 6.2 } = 6.11 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 18.93 }{ 6.38 } = 5.94 ; ;

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{ 10.1**2-6.2**2-6.38**2 }{ 2 * 6.2 * 6.38 } ) = 106° 48'40" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 6.2**2-10.1**2-6.38**2 }{ 2 * 10.1 * 6.38 } ) = 35° 59'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 6.38**2-10.1**2-6.2**2 }{ 2 * 6.2 * 10.1 } ) = 37° 12' ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 18.93 }{ 11.34 } = 1.67 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10.1 }{ 2 * sin 106° 48'40" } = 5.28 ; ;




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