Triangle calculator SAS

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


Right scalene triangle.

Sides: a = 4.445   b = 60   c = 60.16444249121

Area: T = 133.35
Perimeter: p = 124.6099424912
Semiperimeter: s = 62.3054712456

Angle ∠ A = α = 4.23769224201° = 4°14'13″ = 0.07439482464 rad
Angle ∠ B = β = 85.76330775799° = 85°45'47″ = 1.49768480804 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 60
Height: hb = 4.445
Height: hc = 4.43328521446

Median: ma = 60.04111484421
Median: mb = 30.32875126741
Median: mc = 30.0822212456

Inradius: r = 2.1440287544
Circumradius: R = 30.0822212456

Vertex coordinates: A[60.16444249121; 0] B[0; 0] C[0.3288400463; 4.43328521446]
Centroid: CG[20.1644275125; 1.47876173815]
Coordinates of the circumscribed circle: U[30.0822212456; -0]
Coordinates of the inscribed circle: I[2.3054712456; 2.1440287544]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 175.763307758° = 175°45'47″ = 0.07439482464 rad
∠ B' = β' = 94.23769224201° = 94°14'13″ = 1.49768480804 rad
∠ C' = γ' = 90° = 1.57107963268 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 = 4.45 ; ; b = 60 ; ; gamma = 90° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 4.45**2+60**2 - 2 * 4.45 * 60 * cos(90° ) } ; ; c = 60.16 ; ;


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 = 4.45 ; ; b = 60 ; ; c = 60.16 ; ;

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

p = a+b+c = 4.45+60+60.16 = 124.61 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 124.61 }{ 2 } = 62.3 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 62.3 * (62.3-4.45)(62.3-60)(62.3-60.16) } ; ; T = sqrt{ 17782.22 } = 133.35 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 133.35 }{ 4.45 } = 60 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 133.35 }{ 60 } = 4.44 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 133.35 }{ 60.16 } = 4.43 ; ;

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{ 4.45**2-60**2-60.16**2 }{ 2 * 60 * 60.16 } ) = 4° 14'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 60**2-4.45**2-60.16**2 }{ 2 * 4.45 * 60.16 } ) = 85° 45'47" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 60.16**2-4.45**2-60**2 }{ 2 * 60 * 4.45 } ) = 90° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 133.35 }{ 62.3 } = 2.14 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4.45 }{ 2 * sin 4° 14'13" } = 30.08 ; ;




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

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