Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 50   b = 35   c = 16.45

Area: T = 140.7877497668
Perimeter: p = 101.45
Semiperimeter: s = 50.725

Angle ∠ A = α = 150.7211331468° = 150°43'17″ = 2.63105834871 rad
Angle ∠ B = β = 20.02195293994° = 20°1'10″ = 0.34994067027 rad
Angle ∠ C = γ = 9.25991391329° = 9°15'33″ = 0.16216024638 rad

Height: ha = 5.63114999067
Height: hb = 8.04549998667
Height: hc = 17.11770209931

Median: ma = 11.08215725418
Median: mb = 32.84989155072
Median: mc = 42.36656626881

Inradius: r = 2.7765505129
Circumradius: R = 51.11987081183

Vertex coordinates: A[16.45; 0] B[0; 0] C[46.97987993921; 17.11770209931]
Centroid: CG[21.14329331307; 5.70656736644]
Coordinates of the circumscribed circle: U[8.225; 50.45326678649]
Coordinates of the inscribed circle: I[15.725; 2.7765505129]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 29.27986685323° = 29°16'43″ = 2.63105834871 rad
∠ B' = β' = 159.9880470601° = 159°58'50″ = 0.34994067027 rad
∠ C' = γ' = 170.7410860867° = 170°44'27″ = 0.16216024638 rad

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How did we calculate this triangle?

a = 50 ; ; b = 35 ; ; c = 16.45 ; ;

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

p = a+b+c = 50+35+16.45 = 101.45 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 101.45 }{ 2 } = 50.73 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 50.73 * (50.73-50)(50.73-35)(50.73-16.45) } ; ; T = sqrt{ 19821.12 } = 140.79 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 140.79 }{ 50 } = 5.63 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 140.79 }{ 35 } = 8.04 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 140.79 }{ 16.45 } = 17.12 ; ;

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{ 35**2+16.45**2-50**2 }{ 2 * 35 * 16.45 } ) = 150° 43'17" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 50**2+16.45**2-35**2 }{ 2 * 50 * 16.45 } ) = 20° 1'10" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 50**2+35**2-16.45**2 }{ 2 * 50 * 35 } ) = 9° 15'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 140.79 }{ 50.73 } = 2.78 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 50 }{ 2 * sin 150° 43'17" } = 51.12 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 35**2+2 * 16.45**2 - 50**2 } }{ 2 } = 11.082 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 16.45**2+2 * 50**2 - 35**2 } }{ 2 } = 32.849 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 35**2+2 * 50**2 - 16.45**2 } }{ 2 } = 42.366 ; ;
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