Triangle calculator SAS

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


Acute scalene triangle.

Sides: a = 300   b = 250   c = 261.9566226266

Area: T = 31088.90989708
Perimeter: p = 811.9566226266
Semiperimeter: s = 405.9788113133

Angle ∠ A = α = 71.70223382509° = 71°42'8″ = 1.25114418839 rad
Angle ∠ B = β = 52.29876617491° = 52°17'52″ = 0.91327663886 rad
Angle ∠ C = γ = 56° = 0.97773843811 rad

Height: ha = 207.2599393139
Height: hb = 248.7111271767
Height: hc = 237.3659572735

Median: ma = 207.5110318393
Median: mb = 252.3659925978
Median: mc = 243.094408442

Inradius: r = 76.57877956129
Circumradius: R = 157.9888150922

Vertex coordinates: A[261.9566226266; 0] B[0; 0] C[183.4687798894; 237.3659572735]
Centroid: CG[148.4754675053; 79.12198575782]
Coordinates of the circumscribed circle: U[130.9788113133; 88.34658528281]
Coordinates of the inscribed circle: I[155.9788113133; 76.57877956129]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 108.2987661749° = 108°17'52″ = 1.25114418839 rad
∠ B' = β' = 127.7022338251° = 127°42'8″ = 0.91327663886 rad
∠ C' = γ' = 124° = 0.97773843811 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 = 250 ; ; gamma = 56° ; ; ; ; c**2 = a**2+b**2 - 2ab cos gamma ; ; c = sqrt{ a**2+b**2 - 2ab cos gamma } ; ; c = sqrt{ 300**2+250**2 - 2 * 300 * 250 * cos(56° ) } ; ; c = 261.96 ; ;


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 = 250 ; ; c = 261.96 ; ;

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

p = a+b+c = 300+250+261.96 = 811.96 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 811.96 }{ 2 } = 405.98 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 405.98 * (405.98-300)(405.98-250)(405.98-261.96) } ; ; T = sqrt{ 966520261 } = 31088.91 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 31088.91 }{ 300 } = 207.26 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 31088.91 }{ 250 } = 248.71 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 31088.91 }{ 261.96 } = 237.36 ; ;

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**2-250**2-261.96**2 }{ 2 * 250 * 261.96 } ) = 71° 42'8" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 250**2-300**2-261.96**2 }{ 2 * 300 * 261.96 } ) = 52° 17'52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 261.96**2-300**2-250**2 }{ 2 * 250 * 300 } ) = 56° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 31088.91 }{ 405.98 } = 76.58 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 300 }{ 2 * sin 71° 42'8" } = 157.99 ; ;




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

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