Triangle calculator

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

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

Acute scalene triangle.

Sides: a = 956.2187782649   b = 857.3211409974   c = 700

Area: T = 289838.1121964
Perimeter: p = 2513.539919262
Semiperimeter: s = 1256.776959631

Angle ∠ A = α = 75° = 1.3098996939 rad
Angle ∠ B = β = 60° = 1.04771975512 rad
Angle ∠ C = γ = 45° = 0.78553981634 rad

Height: ha = 606.2187782649
Height: hb = 676.1488078402
Height: hc = 828.1098891325

Median: ma = 619.6066236279
Median: mb = 720.018821083
Median: mc = 837.965955984

Inradius: r = 230.6221517909
Circumradius: R = 494.9754746831

Vertex coordinates: A[700; 0] B[0; 0] C[478.1098891325; 828.1098891325]
Centroid: CG[392.7032963775; 276.0366297108]
Coordinates of the circumscribed circle: U[350; 350]
Coordinates of the inscribed circle: I[399.4488186337; 230.6221517909]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 105° = 1.3098996939 rad
∠ B' = β' = 120° = 1.04771975512 rad
∠ C' = γ' = 135° = 0.78553981634 rad

Calculate another triangle




How did we calculate this triangle?

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

c = 700 ; ; alpha = 75° ; ; beta = 60° ; ;

2. From angle α and angle β we calculate angle γ:

 alpha + beta + gamma = 180° ; ; gamma = 180° - alpha - beta = 180° - 75 ° - 60 ° = 45 ° ; ;

3. 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 = 700 * fraction{ sin 75° }{ sin 45° } = 956.22 ; ;

4. 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{ 956.22**2+700**2 - 2 * 956.22 * 700 * cos(60° ) } ; ; b = 857.32 ; ;


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 = 956.22 ; ; b = 857.32 ; ; c = 700 ; ;

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

p = a+b+c = 956.22+857.32+700 = 2513.54 ; ;

6. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 2513.54 }{ 2 } = 1256.77 ; ;

7. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1256.77 * (1256.77-956.22)(1256.77-857.32)(1256.77-700) } ; ; T = sqrt{ 84006131146.6 } = 289838.11 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 289838.11 }{ 956.22 } = 606.22 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 289838.11 }{ 857.32 } = 676.15 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 289838.11 }{ 700 } = 828.11 ; ;

9. 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{ 857.32**2+700**2-956.22**2 }{ 2 * 857.32 * 700 } ) = 75° ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 956.22**2+700**2-857.32**2 }{ 2 * 956.22 * 700 } ) = 60° ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 956.22**2+857.32**2-700**2 }{ 2 * 956.22 * 857.32 } ) = 45° ; ;

10. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 289838.11 }{ 1256.77 } = 230.62 ; ;

11. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 956.22 }{ 2 * sin 75° } = 494.97 ; ;

12. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 857.32**2+2 * 700**2 - 956.22**2 } }{ 2 } = 619.606 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 700**2+2 * 956.22**2 - 857.32**2 } }{ 2 } = 720.018 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 857.32**2+2 * 956.22**2 - 700**2 } }{ 2 } = 837.96 ; ;
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.