Triangle calculator

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

You have entered side a, angle β and angle γ.

Right scalene triangle.

Sides: a = 39   b = 22.51766604984   c = 45.03333209968

Area: T = 439.0754879719
Perimeter: p = 106.5549981495
Semiperimeter: s = 53.27549907476

Angle ∠ A = α = 60° = 1.04771975512 rad
Angle ∠ B = β = 30° = 0.52435987756 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 22.51766604984
Height: hb = 39
Height: hc = 19.5

Median: ma = 29.78767420172
Median: mb = 40.59224869896
Median: mc = 22.51766604984

Inradius: r = 8.24216697508
Circumradius: R = 22.51766604984

Vertex coordinates: A[45.03333209968; 0] B[0; 0] C[33.77549907476; 19.5]
Centroid: CG[26.26994372481; 6.5]
Coordinates of the circumscribed circle: U[22.51766604984; 0]
Coordinates of the inscribed circle: I[30.75883302492; 8.24216697508]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 120° = 1.04771975512 rad
∠ B' = β' = 150° = 0.52435987756 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 = 39 ; ; b = 22.52 ; ; c = 45.03 ; ;

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

p = a+b+c = 39+22.52+45.03 = 106.55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 106.55 }{ 2 } = 53.27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 53.27 * (53.27-39)(53.27-22.52)(53.27-45.03) } ; ; T = sqrt{ 192786.75 } = 439.07 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 439.07 }{ 39 } = 22.52 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 439.07 }{ 22.52 } = 39 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 439.07 }{ 45.03 } = 19.5 ; ;

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{ 39**2-22.52**2-45.03**2 }{ 2 * 22.52 * 45.03 } ) = 60° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22.52**2-39**2-45.03**2 }{ 2 * 39 * 45.03 } ) = 30° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 45.03**2-39**2-22.52**2 }{ 2 * 22.52 * 39 } ) = 90° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 439.07 }{ 53.27 } = 8.24 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 39 }{ 2 * sin 60° } = 22.52 ; ;




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