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

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How did we calculate this triangle?

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 ; ;

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

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

2. Semiperimeter of the triangle

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

3. 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 ; ;

4. 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 ; ;

5. 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{ 956.22**2-857.32**2-700**2 }{ 2 * 857.32 * 700 } ) = 75° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 857.32**2-956.22**2-700**2 }{ 2 * 956.22 * 700 } ) = 60° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 700**2-956.22**2-857.32**2 }{ 2 * 857.32 * 956.22 } ) = 45° ; ;

6. Inradius

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

7. Circumradius

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




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