Triangle calculator

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side b, c and angle α.

Obtuse scalene triangle.

Sides: a = 12.07989388927   b = 11.5   c = 0.8

Area: T = 3.25326911935
Perimeter: p = 24.37989388927
Semiperimeter: s = 12.18994694464

Angle ∠ A = α = 135° = 2.35661944902 rad
Angle ∠ B = β = 42.31657205937° = 42°18'57″ = 0.73985486497 rad
Angle ∠ C = γ = 2.68442794063° = 2°41'3″ = 0.04768495137 rad

Height: ha = 0.53985723402
Height: hb = 0.56656854249
Height: hc = 8.13217279836

Median: ma = 5.4744468815
Median: mb = 6.34109685685
Median: mc = 11.78662369901

Inradius: r = 0.26768443617
Circumradius: R = 8.54110996006

Vertex coordinates: A[0.8; 0] B[0; 0] C[8.93217279836; 8.13217279836]
Centroid: CG[3.24439093279; 2.71105759945]
Coordinates of the circumscribed circle: U[0.4; 8.53217279836]
Coordinates of the inscribed circle: I[0.68994694464; 0.26768443617]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 45° = 2.35661944902 rad
∠ B' = β' = 137.6844279406° = 137°41'3″ = 0.73985486497 rad
∠ C' = γ' = 177.3165720594° = 177°18'57″ = 0.04768495137 rad

Calculate another triangle




How did we calculate this triangle?

1. Input data entered: side b, c and angle α.

b = 11.5 ; ; c = 0.8 ; ; alpha = 135° ; ;

2. Calculation of the third side a of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos alpha ; ; a = sqrt{ b**2+c**2 - 2bc cos alpha } ; ; a = sqrt{ 11.5**2+0.8**2 - 2 * 11.5 * 0.8 * cos 135° } ; ; a = 12.08 ; ;


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 = 12.08 ; ; b = 11.5 ; ; c = 0.8 ; ;

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

p = a+b+c = 12.08+11.5+0.8 = 24.38 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 24.38 }{ 2 } = 12.19 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12.19 * (12.19-12.08)(12.19-11.5)(12.19-0.8) } ; ; T = sqrt{ 10.58 } = 3.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3.25 }{ 12.08 } = 0.54 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3.25 }{ 11.5 } = 0.57 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3.25 }{ 0.8 } = 8.13 ; ;

7. 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{ 11.5**2+0.8**2-12.08**2 }{ 2 * 11.5 * 0.8 } ) = 135° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 12.08**2+0.8**2-11.5**2 }{ 2 * 12.08 * 0.8 } ) = 42° 18'57" ; ; gamma = 180° - alpha - beta = 180° - 135° - 42° 18'57" = 2° 41'3" ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3.25 }{ 12.19 } = 0.27 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 12.08 }{ 2 * sin 135° } = 8.54 ; ;

10. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 11.5**2+2 * 0.8**2 - 12.08**2 } }{ 2 } = 5.474 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.8**2+2 * 12.08**2 - 11.5**2 } }{ 2 } = 6.341 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 11.5**2+2 * 12.08**2 - 0.8**2 } }{ 2 } = 11.786 ; ;
Calculate another triangle

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

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