Triangle calculator

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

You have entered side a, b and c.

Acute isosceles triangle.

Sides: a = 62   b = 103   c = 103

Area: T = 3044.951123114
Perimeter: p = 268
Semiperimeter: s = 134

Angle ∠ A = α = 35.03218507568° = 35°1'55″ = 0.61114211388 rad
Angle ∠ B = β = 72.48440746216° = 72°29'3″ = 1.26550857574 rad
Angle ∠ C = γ = 72.48440746216° = 72°29'3″ = 1.26550857574 rad

Height: ha = 98.22442332625
Height: hb = 59.1255266624
Height: hc = 59.1255266624

Median: ma = 98.22442332625
Median: mb = 67.63332019056
Median: mc = 67.63332019056

Inradius: r = 22.72435166503
Circumradius: R = 54.0043984799

Vertex coordinates: A[103; 0] B[0; 0] C[18.66601941748; 59.1255266624]
Centroid: CG[40.55333980583; 19.7088422208]
Coordinates of the circumscribed circle: U[51.5; 16.25436264929]
Coordinates of the inscribed circle: I[31; 22.72435166503]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.9688149243° = 144°58'5″ = 0.61114211388 rad
∠ B' = β' = 107.5165925378° = 107°30'57″ = 1.26550857574 rad
∠ C' = γ' = 107.5165925378° = 107°30'57″ = 1.26550857574 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 = 62 ; ; b = 103 ; ; c = 103 ; ;

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

p = a+b+c = 62+103+103 = 268 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 268 }{ 2 } = 134 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 134 * (134-62)(134-103)(134-103) } ; ; T = sqrt{ 9271728 } = 3044.95 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3044.95 }{ 62 } = 98.22 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3044.95 }{ 103 } = 59.13 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3044.95 }{ 103 } = 59.13 ; ;

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{ 62**2-103**2-103**2 }{ 2 * 103 * 103 } ) = 35° 1'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 103**2-62**2-103**2 }{ 2 * 62 * 103 } ) = 72° 29'3" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 103**2-62**2-103**2 }{ 2 * 103 * 62 } ) = 72° 29'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3044.95 }{ 134 } = 22.72 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 62 }{ 2 * sin 35° 1'55" } = 54 ; ;




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