Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 45   b = 70.35   c = 99

Area: T = 1416.348776472
Perimeter: p = 214.35
Semiperimeter: s = 107.175

Angle ∠ A = α = 23.99992540859° = 23°59'57″ = 0.41988660018 rad
Angle ∠ B = β = 39.48327856356° = 39°28'58″ = 0.68991046072 rad
Angle ∠ C = γ = 116.5187960278° = 116°31'5″ = 2.03436220446 rad

Height: ha = 62.94987895431
Height: hb = 40.26657502408
Height: hc = 28.61330861559

Median: ma = 82.87882917898
Median: mb = 68.37992320445
Median: mc = 32.21995535683

Inradius: r = 13.21552812197
Circumradius: R = 55.32199676321

Vertex coordinates: A[99; 0] B[0; 0] C[34.73217045455; 28.61330861559]
Centroid: CG[44.57772348485; 9.53876953853]
Coordinates of the circumscribed circle: U[49.5; -24.69991663587]
Coordinates of the inscribed circle: I[36.825; 13.21552812197]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.0010745914° = 156°3″ = 0.41988660018 rad
∠ B' = β' = 140.5177214364° = 140°31'2″ = 0.68991046072 rad
∠ C' = γ' = 63.48220397215° = 63°28'55″ = 2.03436220446 rad

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How did we calculate this triangle?

a = 45 ; ; b = 70.35 ; ; c = 99 ; ;

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

p = a+b+c = 45+70.35+99 = 214.35 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 214.35 }{ 2 } = 107.18 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 107.18 * (107.18-45)(107.18-70.35)(107.18-99) } ; ; T = sqrt{ 2006040.99 } = 1416.35 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1416.35 }{ 45 } = 62.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1416.35 }{ 70.35 } = 40.27 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1416.35 }{ 99 } = 28.61 ; ;

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{ 70.35**2+99**2-45**2 }{ 2 * 70.35 * 99 } ) = 23° 59'57" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 45**2+99**2-70.35**2 }{ 2 * 45 * 99 } ) = 39° 28'58" ; ; gamma = 180° - alpha - beta = 180° - 23° 59'57" - 39° 28'58" = 116° 31'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1416.35 }{ 107.18 } = 13.22 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 45 }{ 2 * sin 23° 59'57" } = 55.32 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 70.35**2+2 * 99**2 - 45**2 } }{ 2 } = 82.878 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 99**2+2 * 45**2 - 70.35**2 } }{ 2 } = 68.379 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 70.35**2+2 * 45**2 - 99**2 } }{ 2 } = 32.2 ; ;
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