Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 49.99   b = 111.8   c = 99.99

Area: T = 2499.254998727
Perimeter: p = 261.78
Semiperimeter: s = 130.89

Angle ∠ A = α = 26.56601917446° = 26°33'37″ = 0.46435627959 rad
Angle ∠ B = β = 90.01328369596° = 90°46″ = 1.5711020374 rad
Angle ∠ C = γ = 63.42769712957° = 63°25'37″ = 1.10770094837 rad

Height: ha = 99.99899974904
Height: hb = 44.70993020979
Height: hc = 49.99899987453

Median: ma = 103.0722159311
Median: mb = 55.89899821077
Median: mc = 70.70879912386

Inradius: r = 19.09442775405
Circumradius: R = 55.9900001403

Vertex coordinates: A[99.99; 0] B[0; 0] C[-0.011120012; 49.99899987453]
Centroid: CG[33.32662666267; 16.66333329151]
Coordinates of the circumscribed circle: U[49.995; 25.00662018679]
Coordinates of the inscribed circle: I[19.09; 19.09442775405]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.4439808255° = 153°26'23″ = 0.46435627959 rad
∠ B' = β' = 89.98771630404° = 89°59'14″ = 1.5711020374 rad
∠ C' = γ' = 116.5733028704° = 116°34'23″ = 1.10770094837 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 = 49.99+111.8+99.99 = 261.78 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 261.78 }{ 2 } = 130.89 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 130.89 * (130.89-49.99)(130.89-111.8)(130.89-99.99) } ; ; T = sqrt{ 6246250.5 } = 2499.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2499.25 }{ 49.99 } = 99.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2499.25 }{ 111.8 } = 44.71 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2499.25 }{ 99.99 } = 49.99 ; ;

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{ 111.8**2+99.99**2-49.99**2 }{ 2 * 111.8 * 99.99 } ) = 26° 33'37" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 49.99**2+99.99**2-111.8**2 }{ 2 * 49.99 * 99.99 } ) = 90° 46" ; ;
 gamma = 180° - alpha - beta = 180° - 26° 33'37" - 90° 46" = 63° 25'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2499.25 }{ 130.89 } = 19.09 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 49.99 }{ 2 * sin 26° 33'37" } = 55.9 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 111.8**2+2 * 99.99**2 - 49.99**2 } }{ 2 } = 103.072 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 99.99**2+2 * 49.99**2 - 111.8**2 } }{ 2 } = 55.89 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 111.8**2+2 * 49.99**2 - 99.99**2 } }{ 2 } = 70.708 ; ;
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