Triangle calculator

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

You have entered side c, angle α, angle β and angle γ.

Obtuse isosceles triangle.

Sides: a = 51.38441739579   b = 51.38441739579   c = 89

Area: T = 1143.298787056
Perimeter: p = 191.7688347916
Semiperimeter: s = 95.88441739579

Angle ∠ A = α = 30° = 0.52435987756 rad
Angle ∠ B = β = 30° = 0.52435987756 rad
Angle ∠ C = γ = 120° = 2.09443951024 rad

Height: ha = 44.5
Height: hb = 44.5
Height: hc = 25.69220869789

Median: ma = 67.97548728085
Median: mb = 67.97548728085
Median: mc = 25.69220869789

Inradius: r = 11.92437390632
Circumradius: R = 51.38441739579

Vertex coordinates: A[89; 0] B[0; 0] C[44.5; 25.69220869789]
Centroid: CG[44.5; 8.5644028993]
Coordinates of the circumscribed circle: U[44.5; -25.69220869789]
Coordinates of the inscribed circle: I[44.5; 11.92437390632]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150° = 0.52435987756 rad
∠ B' = β' = 150° = 0.52435987756 rad
∠ C' = γ' = 60° = 2.09443951024 rad

Calculate another triangle


How did we calculate this triangle?

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

c = 89 ; ; alpha = 30° ; ; beta = 30° ; ; gamma = 120° ; ;

2. From angle α, angle γ and side c we calculate side a - By using the law of sines, we calculate unknown side a:

 fraction{ a }{ c } = fraction{ sin alpha }{ sin gamma } ; ; ; ; a = c * fraction{ sin alpha }{ sin gamma } ; ; ; ; a = 89 * fraction{ sin 30° }{ sin 120° } = 51.38 ; ;

3. Calculation of the third side b of the triangle using a Law of Cosines

b**2 = a**2+c**2 - 2ac cos beta ; ; b = sqrt{ a**2+c**2 - 2ac cos beta } ; ; b = sqrt{ 51.38**2+89**2 - 2 * 51.38 * 89 * cos 30° } ; ; b = 51.38 ; ;
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 = 51.38 ; ; b = 51.38 ; ; c = 89 ; ;

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

p = a+b+c = 51.38+51.38+89 = 191.77 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 191.77 }{ 2 } = 95.88 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 95.88 * (95.88-51.38)(95.88-51.38)(95.88-89) } ; ; T = sqrt{ 1307130.02 } = 1143.3 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1143.3 }{ 51.38 } = 44.5 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1143.3 }{ 51.38 } = 44.5 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1143.3 }{ 89 } = 25.69 ; ;

8. 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{ 51.38**2+89**2-51.38**2 }{ 2 * 51.38 * 89 } ) = 30° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 51.38**2+89**2-51.38**2 }{ 2 * 51.38 * 89 } ) = 30° ; ;
 gamma = 180° - alpha - beta = 180° - 30° - 30° = 120° ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1143.3 }{ 95.88 } = 11.92 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 51.38 }{ 2 * sin 30° } = 51.38 ; ;

11. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 51.38**2+2 * 89**2 - 51.38**2 } }{ 2 } = 67.975 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 89**2+2 * 51.38**2 - 51.38**2 } }{ 2 } = 67.975 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 51.38**2+2 * 51.38**2 - 89**2 } }{ 2 } = 25.692 ; ;
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.