Triangle calculator SAS

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


Obtuse scalene triangle.

Sides: a = 232   b = 100   c = 171.2955300863

Area: T = 7761.915503376
Perimeter: p = 503.2955300863
Semiperimeter: s = 251.6487650432

Angle ∠ A = α = 115.0066302744° = 115°23″ = 2.00772386434 rad
Angle ∠ B = β = 22.99436972559° = 22°59'37″ = 0.40113157243 rad
Angle ∠ C = γ = 42° = 0.73330382858 rad

Height: ha = 66.91330606359
Height: hb = 155.2388300675
Height: hc = 90.62661292008

Median: ma = 78.83655252974
Median: mb = 197.6944309602
Median: mc = 156.7698874384

Inradius: r = 30.84443771299
Circumradius: R = 127.9988405121

Vertex coordinates: A[171.2955300863; 0] B[0; 0] C[213.5677096497; 90.62661292008]
Centroid: CG[128.2877465787; 30.20987097336]
Coordinates of the circumscribed circle: U[85.64876504317; 95.12113524351]
Coordinates of the inscribed circle: I[151.6487650432; 30.84443771299]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 64.99436972559° = 64°59'37″ = 2.00772386434 rad
∠ B' = β' = 157.0066302744° = 157°23″ = 0.40113157243 rad
∠ C' = γ' = 138° = 0.73330382858 rad

Calculate another triangle




How did we calculate this triangle?

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

a = 232 ; ; b = 100 ; ; gamma = 42° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 232**2+100**2 - 2 * 232 * 100 * cos(42° ) } ; ; c = 171.3 ; ;


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 = 232 ; ; b = 100 ; ; c = 171.3 ; ;

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

p = a+b+c = 232+100+171.3 = 503.3 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 503.3 }{ 2 } = 251.65 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 251.65 * (251.65-232)(251.65-100)(251.65-171.3) } ; ; T = sqrt{ 60247324.99 } = 7761.92 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 7761.92 }{ 232 } = 66.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 7761.92 }{ 100 } = 155.24 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 7761.92 }{ 171.3 } = 90.63 ; ;

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{ 232**2-100**2-171.3**2 }{ 2 * 100 * 171.3 } ) = 115° 23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 100**2-232**2-171.3**2 }{ 2 * 232 * 171.3 } ) = 22° 59'37" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 171.3**2-232**2-100**2 }{ 2 * 100 * 232 } ) = 42° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 7761.92 }{ 251.65 } = 30.84 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 232 }{ 2 * sin 115° 23" } = 128 ; ;




Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.