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 = 430.8660000999   b = 429.1277215462   c = 66

Area: T = 14143.06326736
Perimeter: p = 925.9877216461
Semiperimeter: s = 462.9943608231

Angle ∠ A = α = 87.1° = 87°6' = 1.52201817785 rad
Angle ∠ B = β = 84.1° = 84°6' = 1.46878219009 rad
Angle ∠ C = γ = 8.8° = 8°48' = 0.15435889742 rad

Height: ha = 65.65503859297
Height: hb = 65.91554775742
Height: hc = 428.5787656777

Median: ma = 218.7330424061
Median: mb = 221.2770487114
Median: mc = 428.7266315679

Inradius: r = 30.54769933541
Circumradius: R = 215.706624315

Vertex coordinates: A[66; 0] B[0; 0] C[44.28991925028; 428.5787656777]
Centroid: CG[36.76330641676; 142.8599218926]
Coordinates of the circumscribed circle: U[33; 213.1677031536]
Coordinates of the inscribed circle: I[33.86663927683; 30.54769933541]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 92.9° = 92°54' = 1.52201817785 rad
∠ B' = β' = 95.9° = 95°54' = 1.46878219009 rad
∠ C' = γ' = 171.2° = 171°12' = 0.15435889742 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 = 430.86 ; ; b = 429.13 ; ; c = 66 ; ;

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

p = a+b+c = 430.86+429.13+66 = 925.99 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 925.99 }{ 2 } = 462.99 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 462.99 * (462.99-430.86)(462.99-429.13)(462.99-66) } ; ; T = sqrt{ 200026221.79 } = 14143.06 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 14143.06 }{ 430.86 } = 65.65 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 14143.06 }{ 429.13 } = 65.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 14143.06 }{ 66 } = 428.58 ; ;

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{ 430.86**2-429.13**2-66**2 }{ 2 * 429.13 * 66 } ) = 87° 6' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 429.13**2-430.86**2-66**2 }{ 2 * 430.86 * 66 } ) = 84° 6' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 66**2-430.86**2-429.13**2 }{ 2 * 429.13 * 430.86 } ) = 8° 48' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 14143.06 }{ 462.99 } = 30.55 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 430.86 }{ 2 * sin 87° 6' } = 215.71 ; ;




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