Triangle calculator SAS

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


Obtuse scalene triangle.

Sides: a = 250   b = 360   c = 207.0598535057

Area: T = 25163.68106562
Perimeter: p = 817.0598535057
Semiperimeter: s = 408.5299267529

Angle ∠ A = α = 42.46767959259° = 42°28' = 0.74111854117 rad
Angle ∠ B = β = 103.5333204074° = 103°32' = 1.80769952962 rad
Angle ∠ C = γ = 34° = 0.59334119457 rad

Height: ha = 201.3099445249
Height: hb = 139.7988225868
Height: hc = 243.0598617692

Median: ma = 265.7288467557
Median: mb = 142.4311100782
Median: mc = 292.1165885848

Inradius: r = 61.59657843324
Circumradius: R = 185.1410524649

Vertex coordinates: A[207.0598535057; 0] B[0; 0] C[-58.50222082118; 243.0598617692]
Centroid: CG[49.51987756152; 81.02195392307]
Coordinates of the circumscribed circle: U[103.5299267529; 153.4888451137]
Coordinates of the inscribed circle: I[48.52992675287; 61.59657843324]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.5333204074° = 137°32' = 0.74111854117 rad
∠ B' = β' = 76.46767959259° = 76°28' = 1.80769952962 rad
∠ C' = γ' = 146° = 0.59334119457 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 = 250 ; ; b = 360 ; ; gamma = 34° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 250**2+360**2 - 2 * 250 * 360 * cos(34° ) } ; ; c = 207.06 ; ;


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 = 250 ; ; b = 360 ; ; c = 207.06 ; ;

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

p = a+b+c = 250+360+207.06 = 817.06 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 817.06 }{ 2 } = 408.53 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 408.53 * (408.53-250)(408.53-360)(408.53-207.06) } ; ; T = sqrt{ 633210824.17 } = 25163.68 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 25163.68 }{ 250 } = 201.31 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 25163.68 }{ 360 } = 139.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 25163.68 }{ 207.06 } = 243.06 ; ;

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{ 250**2-360**2-207.06**2 }{ 2 * 360 * 207.06 } ) = 42° 28' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 360**2-250**2-207.06**2 }{ 2 * 250 * 207.06 } ) = 103° 32' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 207.06**2-250**2-360**2 }{ 2 * 360 * 250 } ) = 34° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 25163.68 }{ 408.53 } = 61.6 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 250 }{ 2 * sin 42° 28' } = 185.14 ; ;




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