Triangle calculator SAS

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


Right scalene triangle.

Sides: a = 0.472   b = 0.015   c = 0.47222382873

Area: T = 0.004354
Perimeter: p = 0.95992382873
Semiperimeter: s = 0.48796191437

Angle ∠ A = α = 88.18797721622° = 88°10'47″ = 1.53990273579 rad
Angle ∠ B = β = 1.82202278378° = 1°49'13″ = 0.03217689689 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 0.015
Height: hb = 0.472
Height: hc = 0.01549924311

Median: ma = 0.23664762144
Median: mb = 0.47220595831
Median: mc = 0.23661191437

Inradius: r = 0.00773808563
Circumradius: R = 0.23661191437

Vertex coordinates: A[0.47222382873; 0] B[0; 0] C[0.47217618329; 0.01549924311]
Centroid: CG[0.31546667067; 0.0054997477]
Coordinates of the circumscribed circle: U[0.23661191437; 0]
Coordinates of the inscribed circle: I[0.46546191437; 0.00773808563]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 91.82202278378° = 91°49'13″ = 1.53990273579 rad
∠ B' = β' = 178.1879772162° = 178°10'47″ = 0.03217689689 rad
∠ C' = γ' = 90° = 1.57107963268 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 = 0.47 ; ; b = 0.02 ; ; gamma = 90° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 0.47**2+0.02**2 - 2 * 0.47 * 0.02 * cos(90° ) } ; ; c = 0.47 ; ;


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 = 0.47 ; ; b = 0.02 ; ; c = 0.47 ; ;

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

p = a+b+c = 0.47+0.02+0.47 = 0.96 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 0.96 }{ 2 } = 0.48 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 0.48 * (0.48-0.47)(0.48-0.02)(0.48-0.47) } ; ; T = sqrt{ 0 } = 0 ; ;

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 }{ 0.47 } = 0.02 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0 }{ 0.02 } = 0.47 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0 }{ 0.47 } = 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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 0.47**2-0.02**2-0.47**2 }{ 2 * 0.02 * 0.47 } ) = 88° 10'47" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 0.02**2-0.47**2-0.47**2 }{ 2 * 0.47 * 0.47 } ) = 1° 49'13" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 0.47**2-0.47**2-0.02**2 }{ 2 * 0.02 * 0.47 } ) = 90° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0 }{ 0.48 } = 0.01 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 0.47 }{ 2 * sin 88° 10'47" } = 0.24 ; ;




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