Triangle calculator SAS

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


Right scalene triangle.

Sides: a = 76   b = 157   c = 174.4287635425

Area: T = 5966
Perimeter: p = 407.4287635425
Semiperimeter: s = 203.7143817713

Angle ∠ A = α = 25.83105301428° = 25°49'50″ = 0.45108277985 rad
Angle ∠ B = β = 64.16994698572° = 64°10'10″ = 1.12199685283 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 157
Height: hb = 76
Height: hc = 68.40765914837

Median: ma = 161.5333278305
Median: mb = 109.2622299079
Median: mc = 87.21438177126

Inradius: r = 29.28661822874
Circumradius: R = 87.21438177126

Vertex coordinates: A[174.4287635425; 0] B[0; 0] C[33.11440188074; 68.40765914837]
Centroid: CG[69.18105514108; 22.80221971612]
Coordinates of the circumscribed circle: U[87.21438177126; 0]
Coordinates of the inscribed circle: I[46.71438177126; 29.28661822874]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.1699469857° = 154°10'10″ = 0.45108277985 rad
∠ B' = β' = 115.8310530143° = 115°49'50″ = 1.12199685283 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 = 76 ; ; b = 157 ; ; gamma = 90° ; ; ; ; c**2 = a**2+b**2 - 2ab cos gamma ; ; c = sqrt{ a**2+b**2 - 2ab cos gamma } ; ; c = sqrt{ 76**2+157**2 - 2 * 76 * 157 * cos 90° } ; ; c = 174.43 ; ;
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 = 76 ; ; b = 157 ; ; c = 174.43 ; ;

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

p = a+b+c = 76+157+174.43 = 407.43 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 407.43 }{ 2 } = 203.71 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 203.71 * (203.71-76)(203.71-157)(203.71-174.43) } ; ; T = sqrt{ 35593156 } = 5966 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5966 }{ 76 } = 157 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5966 }{ 157 } = 76 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5966 }{ 174.43 } = 68.41 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 157**2+174.43**2-76**2 }{ 2 * 157 * 174.43 } ) = 25° 49'50" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 76**2+174.43**2-157**2 }{ 2 * 76 * 174.43 } ) = 64° 10'10" ; ;
 gamma = 180° - alpha - beta = 180° - 25° 49'50" - 64° 10'10" = 90° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5966 }{ 203.71 } = 29.29 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 76 }{ 2 * sin 25° 49'50" } = 87.21 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 157**2+2 * 174.43**2 - 76**2 } }{ 2 } = 161.533 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 174.43**2+2 * 76**2 - 157**2 } }{ 2 } = 109.262 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 157**2+2 * 76**2 - 174.43**2 } }{ 2 } = 87.214 ; ;
Calculate another triangle


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

See more information about triangles or more details on solving triangles.