Triangle calculator SAS

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


Acute scalene triangle.

Sides: a = 300   b = 400   c = 283.3632616651

Area: T = 42426.40768712
Perimeter: p = 983.3632616651
Semiperimeter: s = 491.6811308325

Angle ∠ A = α = 48.47113182445° = 48°28'17″ = 0.84659840961 rad
Angle ∠ B = β = 86.52986817555° = 86°31'43″ = 1.5110210394 rad
Angle ∠ C = γ = 45° = 0.78553981634 rad

Height: ha = 282.8432712475
Height: hb = 212.1322034356
Height: hc = 299.4549570114

Median: ma = 312.4855497676
Median: mb = 212.4798672477
Median: mc = 323.9233458353

Inradius: r = 86.28884273874
Circumradius: R = 200.3687627769

Vertex coordinates: A[283.3632616651; 0] B[0; 0] C[18.16546623625; 299.4549570114]
Centroid: CG[100.5099093005; 99.81765233712]
Coordinates of the circumscribed circle: U[141.6811308325; 141.6811308325]
Coordinates of the inscribed circle: I[91.68113083254; 86.28884273874]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131.5298681755° = 131°31'43″ = 0.84659840961 rad
∠ B' = β' = 93.47113182445° = 93°28'17″ = 1.5110210394 rad
∠ C' = γ' = 135° = 0.78553981634 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 = 300 ; ; b = 400 ; ; gamma = 45° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 300**2+400**2 - 2 * 300 * 400 * cos(45° ) } ; ; c = 283.36 ; ;


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 = 300 ; ; b = 400 ; ; c = 283.36 ; ;

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

p = a+b+c = 300+400+283.36 = 983.36 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 983.36 }{ 2 } = 491.68 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 491.68 * (491.68-300)(491.68-400)(491.68-283.36) } ; ; T = sqrt{ 1800000000 } = 42426.41 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 42426.41 }{ 300 } = 282.84 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 42426.41 }{ 400 } = 212.13 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 42426.41 }{ 283.36 } = 299.45 ; ;

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{ 300**2-400**2-283.36**2 }{ 2 * 400 * 283.36 } ) = 48° 28'17" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 400**2-300**2-283.36**2 }{ 2 * 300 * 283.36 } ) = 86° 31'43" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 283.36**2-300**2-400**2 }{ 2 * 400 * 300 } ) = 45° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 42426.41 }{ 491.68 } = 86.29 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 300 }{ 2 * sin 48° 28'17" } = 200.37 ; ;




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

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