Triangle calculator SAS

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


Right scalene triangle.

Sides: a = 1500   b = 141.5   c = 1506.659930124

Area: T = 106125
Perimeter: p = 3148.159930124
Semiperimeter: s = 1574.087965062

Angle ∠ A = α = 84.61110454122° = 84°36'40″ = 1.4776741326 rad
Angle ∠ B = β = 5.38989545878° = 5°23'20″ = 0.09440550008 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 141.5
Height: hb = 1500
Height: hc = 140.8754582479

Median: ma = 763.2311452444
Median: mb = 1501.668759388
Median: mc = 753.3329650618

Inradius: r = 67.42203493822
Circumradius: R = 753.3329650618

Vertex coordinates: A[1506.659930124; 0] B[0; 0] C[1493.377013229; 140.8754582479]
Centroid: CG[1000.010981117; 46.95881941597]
Coordinates of the circumscribed circle: U[753.3329650618; 0]
Coordinates of the inscribed circle: I[1432.587965062; 67.42203493822]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 95.38989545878° = 95°23'20″ = 1.4776741326 rad
∠ B' = β' = 174.6111045412° = 174°36'40″ = 0.09440550008 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 = 1500 ; ; b = 141.5 ; ; gamma = 90° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 1500**2+141.5**2 - 2 * 1500 * 141.5 * cos(90° ) } ; ; c = 1506.66 ; ;


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 = 1500 ; ; b = 141.5 ; ; c = 1506.66 ; ;

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

p = a+b+c = 1500+141.5+1506.66 = 3148.16 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 3148.16 }{ 2 } = 1574.08 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1574.08 * (1574.08-1500)(1574.08-141.5)(1574.08-1506.66) } ; ; T = sqrt{ 11262515625 } = 106125 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 106125 }{ 1500 } = 141.5 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 106125 }{ 141.5 } = 1500 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 106125 }{ 1506.66 } = 140.87 ; ;

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{ 1500**2-141.5**2-1506.66**2 }{ 2 * 141.5 * 1506.66 } ) = 84° 36'40" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 141.5**2-1500**2-1506.66**2 }{ 2 * 1500 * 1506.66 } ) = 5° 23'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 1506.66**2-1500**2-141.5**2 }{ 2 * 141.5 * 1500 } ) = 90° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 106125 }{ 1574.08 } = 67.42 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1500 }{ 2 * sin 84° 36'40" } = 753.33 ; ;




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

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