Triangle calculator

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

You have entered side a, b and c.

Right scalene triangle.

Sides: a = 12   b = 35   c = 37

Area: T = 210
Perimeter: p = 84
Semiperimeter: s = 42

Angle ∠ A = α = 18.92546444161° = 18°55'29″ = 0.33302973548 rad
Angle ∠ B = β = 71.07553555839° = 71°4'31″ = 1.2440498972 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 35
Height: hb = 12
Height: hc = 11.35113513514

Median: ma = 35.51105618091
Median: mb = 21.21990951739
Median: mc = 18.5

Inradius: r = 5
Circumradius: R = 18.5

Vertex coordinates: A[37; 0] B[0; 0] C[3.89218918919; 11.35113513514]
Centroid: CG[13.63106306306; 3.78437837838]
Coordinates of the circumscribed circle: U[18.5; 0]
Coordinates of the inscribed circle: I[7; 5]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.0755355584° = 161°4'31″ = 0.33302973548 rad
∠ B' = β' = 108.9254644416° = 108°55'29″ = 1.2440498972 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: side a, b and c.

a = 12 ; ; b = 35 ; ; c = 37 ; ;


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 = 12 ; ; b = 35 ; ; c = 37 ; ; : Nr. 1

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

p = a+b+c = 12+35+37 = 84 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 84 }{ 2 } = 42 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 42 * (42-12)(42-35)(42-37) } ; ; T = sqrt{ 44100 } = 210 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 210 }{ 12 } = 35 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 210 }{ 35 } = 12 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 210 }{ 37 } = 11.35 ; ;

6. 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{ 12**2-35**2-37**2 }{ 2 * 35 * 37 } ) = 18° 55'29" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 35**2-12**2-37**2 }{ 2 * 12 * 37 } ) = 71° 4'31" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 37**2-12**2-35**2 }{ 2 * 35 * 12 } ) = 90° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 210 }{ 42 } = 5 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 18° 55'29" } = 18.5 ; ;




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