Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 10   b = 20   c = 29

Area: T = 52.2732722332
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 10.38443665905° = 10°23'4″ = 0.18112413877 rad
Angle ∠ B = β = 21.1311000091° = 21°7'52″ = 0.36988055258 rad
Angle ∠ C = γ = 148.4854633319° = 148°29'5″ = 2.592154574 rad

Height: ha = 10.45545444664
Height: hb = 5.22772722332
Height: hc = 3.60550153332

Median: ma = 24.40328686838
Median: mb = 19.24883765549
Median: mc = 6.30547601065

Inradius: r = 1.77219566892
Circumradius: R = 27.73991330566

Vertex coordinates: A[29; 0] B[0; 0] C[9.32875862069; 3.60550153332]
Centroid: CG[12.7765862069; 1.20216717777]
Coordinates of the circumscribed circle: U[14.5; -23.64876109308]
Coordinates of the inscribed circle: I[9.5; 1.77219566892]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.616563341° = 169°36'56″ = 0.18112413877 rad
∠ B' = β' = 158.8698999909° = 158°52'8″ = 0.36988055258 rad
∠ C' = γ' = 31.51553666815° = 31°30'55″ = 2.592154574 rad

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How did we calculate this triangle?

a = 10 ; ; b = 20 ; ; c = 29 ; ;

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

p = a+b+c = 10+20+29 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-10)(29.5-20)(29.5-29) } ; ; T = sqrt{ 2732.44 } = 52.27 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 52.27 }{ 10 } = 10.45 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 52.27 }{ 20 } = 5.23 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 52.27 }{ 29 } = 3.61 ; ;

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{ 20**2+29**2-10**2 }{ 2 * 20 * 29 } ) = 10° 23'4" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 10**2+29**2-20**2 }{ 2 * 10 * 29 } ) = 21° 7'52" ; ; gamma = 180° - alpha - beta = 180° - 10° 23'4" - 21° 7'52" = 148° 29'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 52.27 }{ 29.5 } = 1.77 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 10 }{ 2 * sin 10° 23'4" } = 27.74 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 20**2+2 * 29**2 - 10**2 } }{ 2 } = 24.403 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 29**2+2 * 10**2 - 20**2 } }{ 2 } = 19.248 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 20**2+2 * 10**2 - 29**2 } }{ 2 } = 6.305 ; ;
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