Triangle calculator

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

You have entered side a, b and c.

Acute scalene triangle.

Sides: a = 33   b = 51   c = 42

Area: T = 690.1330422457
Perimeter: p = 126
Semiperimeter: s = 63

Angle ∠ A = α = 40.11991668984° = 40°7'9″ = 0.77002115555 rad
Angle ∠ B = β = 84.78440914295° = 84°47'3″ = 1.48797615488 rad
Angle ∠ C = γ = 55.0976741672° = 55°5'48″ = 0.96216195493 rad

Height: ha = 41.82660862095
Height: hb = 27.06439381355
Height: hc = 32.86333534503

Median: ma = 43.7066406853
Median: mb = 27.86112634315
Median: mc = 37.47699879904

Inradius: r = 10.95444511501
Circumradius: R = 25.60660295634

Vertex coordinates: A[42; 0] B[0; 0] C[3; 32.86333534503]
Centroid: CG[15; 10.95444511501]
Coordinates of the circumscribed circle: U[21; 14.65215784133]
Coordinates of the inscribed circle: I[12; 10.95444511501]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.8810833102° = 139°52'51″ = 0.77002115555 rad
∠ B' = β' = 95.21659085705° = 95°12'57″ = 1.48797615488 rad
∠ C' = γ' = 124.9033258328° = 124°54'12″ = 0.96216195493 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 = 33 ; ; b = 51 ; ; c = 42 ; ;

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

p = a+b+c = 33+51+42 = 126 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 126 }{ 2 } = 63 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 63 * (63-33)(63-51)(63-42) } ; ; T = sqrt{ 476280 } = 690.13 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 690.13 }{ 33 } = 41.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 690.13 }{ 51 } = 27.06 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 690.13 }{ 42 } = 32.86 ; ;

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{ 33**2-51**2-42**2 }{ 2 * 51 * 42 } ) = 40° 7'9" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 51**2-33**2-42**2 }{ 2 * 33 * 42 } ) = 84° 47'3" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 42**2-33**2-51**2 }{ 2 * 51 * 33 } ) = 55° 5'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 690.13 }{ 63 } = 10.95 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 33 }{ 2 * sin 40° 7'9" } = 25.61 ; ;




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