Triangle calculator

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

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

Right scalene triangle.

Sides: a = 890.9433320909   b = 170   c = 874.5744182715

Area: T = 74338.80655308
Perimeter: p = 1935.518750362
Semiperimeter: s = 967.7598751812

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 11° = 0.19219862177 rad
Angle ∠ C = γ = 79° = 1.37988101091 rad

Height: ha = 166.8776621186
Height: hb = 874.5744182715
Height: hc = 170

Median: ma = 445.4721660454
Median: mb = 878.6955055791
Median: mc = 469.1699479259

Inradius: r = 76.81554309032
Circumradius: R = 445.4721660454

Vertex coordinates: A[874.5744182715; 0] B[0; 0] C[874.5744182715; 170]
Centroid: CG[583.0499455143; 56.66766666667]
Coordinates of the circumscribed circle: U[437.2877091358; 85]
Coordinates of the inscribed circle: I[797.7598751812; 76.81554309032]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 169° = 0.19219862177 rad
∠ C' = γ' = 101° = 1.37988101091 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 = 890.94 ; ; b = 170 ; ; c = 874.57 ; ;

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

p = a+b+c = 890.94+170+874.57 = 1935.52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1935.52 }{ 2 } = 967.76 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 967.76 * (967.76-890.94)(967.76-170)(967.76-874.57) } ; ; T = sqrt{ 5526258007.74 } = 74338.81 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 74338.81 }{ 890.94 } = 166.88 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 74338.81 }{ 170 } = 874.57 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 74338.81 }{ 874.57 } = 170 ; ;

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{ 890.94**2-170**2-874.57**2 }{ 2 * 170 * 874.57 } ) = 90° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 170**2-890.94**2-874.57**2 }{ 2 * 890.94 * 874.57 } ) = 11° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 874.57**2-890.94**2-170**2 }{ 2 * 170 * 890.94 } ) = 79° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 74338.81 }{ 967.76 } = 76.82 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 890.94 }{ 2 * sin 90° } = 445.47 ; ;




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