Triangle calculator

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

You have entered side a, b and c (hypotenuse-calculated).

Right scalene triangle.

Sides: a = 64   b = 0.8   c = 64.00549998047

Area: T = 25.6
Perimeter: p = 128.8054999805
Semiperimeter: s = 64.40224999024

Angle ∠ A = α = 89.28438400545° = 89°17'2″ = 1.55882969778 rad
Angle ∠ B = β = 0.71661599455° = 0°42'58″ = 0.0122499349 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 0.8
Height: hb = 64
Height: hc = 0.87999375073

Median: ma = 32.0109998438
Median: mb = 64.00112499878
Median: mc = 32.00224999024

Inradius: r = 0.39875000976
Circumradius: R = 32.00224999024

Vertex coordinates: A[64.00549998047; 0] B[0; 0] C[63.99550005859; 0.87999375073]
Centroid: CG[42.66766667969; 0.26766458358]
Coordinates of the circumscribed circle: U[32.00224999024; 0]
Coordinates of the inscribed circle: I[63.60224999024; 0.39875000976]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90.71661599455° = 90°42'58″ = 1.55882969778 rad
∠ B' = β' = 179.2843840055° = 179°17'2″ = 0.0122499349 rad
∠ C' = γ' = 90° = 1.57107963268 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 = 64 ; ; b = 0.8 ; ; c = 64 ; ;

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

p = a+b+c = 64+0.8+64 = 128.8 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 128.8 }{ 2 } = 64.4 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 64.4 * (64.4-64)(64.4-0.8)(64.4-64) } ; ; T = sqrt{ 655.36 } = 25.6 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 25.6 }{ 64 } = 0.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 25.6 }{ 0.8 } = 64 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 25.6 }{ 64 } = 0.8 ; ;

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{ 64**2-0.8**2-64**2 }{ 2 * 0.8 * 64 } ) = 89° 17'2" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 0.8**2-64**2-64**2 }{ 2 * 64 * 64 } ) = 0° 42'58" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 64**2-64**2-0.8**2 }{ 2 * 0.8 * 64 } ) = 90° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 25.6 }{ 64.4 } = 0.4 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 64 }{ 2 * sin 89° 17'2" } = 32 ; ;




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