Triangle calculator SSS - result

Please enter the triangle sides:


Right isosceles triangle.

Sides: a = 600   b = 600   c = 848.53

Area: T = 1800009.999998
Perimeter: p = 2048.53
Semiperimeter: s = 1024.265

Angle ∠ A = α = 454.9998742318° = 45° = 0.78553959683 rad
Angle ∠ B = β = 454.9998742318° = 45° = 0.78553959683 rad
Angle ∠ C = γ = 900.0002515364° = 90°1″ = 1.57108007169 rad

Height: ha = 6009.999999994
Height: hb = 6009.999999994
Height: hc = 424.2633137422

Median: ma = 670.8221571247
Median: mb = 670.8221571247
Median: mc = 424.2633137422

Inradius: r = 175.7365771503
Circumradius: R = 424.2655000004

Vertex coordinates: A[848.53; 0] B[0; 0] C[424.265; 424.2633137422]
Centroid: CG[424.265; 141.4211045807]
Coordinates of the circumscribed circle: U[424.265; -0.00218625823]
Coordinates of the inscribed circle: I[424.265; 175.7365771503]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 1355.000125768° = 135° = 0.78553959683 rad
∠ B' = β' = 1355.000125768° = 135° = 0.78553959683 rad
∠ C' = γ' = 909.9997484636° = 89°59'59″ = 1.57108007169 rad

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How did we calculate this triangle?

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

p = a+b+c = 600+600+848.53 = 2048.53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 2048.53 }{ 2 } = 1024.27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1024.27 * (1024.27-600)(1024.27-600)(1024.27-848.53) } ; ; T = sqrt{ 32399999999.4 } = 180000 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 180000 }{ 600 } = 600 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 180000 }{ 600 } = 600 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 180000 }{ 848.53 } = 424.26 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 600**2+848.53**2-600**2 }{ 2 * 600 * 848.53 } ) = 45° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 600**2+848.53**2-600**2 }{ 2 * 600 * 848.53 } ) = 45° ; ; gamma = 180° - alpha - beta = 180° - 45° - 45° = 90° 1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 180000 }{ 1024.27 } = 175.74 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 600 }{ 2 * sin 45° } = 424.27 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 600**2+2 * 848.53**2 - 600**2 } }{ 2 } = 670.822 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 848.53**2+2 * 600**2 - 600**2 } }{ 2 } = 670.822 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 600**2+2 * 600**2 - 848.53**2 } }{ 2 } = 424.263 ; ;
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