Triangle calculator - result

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side b, c and angle α.

Obtuse scalene triangle.

Sides: a = 23.58108907352   b = 30   c = 14

Area: T = 160.8699333055
Perimeter: p = 67.58108907352
Semiperimeter: s = 33.79904453676

Angle ∠ A = α = 50° = 0.8732664626 rad
Angle ∠ B = β = 102.9487843086° = 102°56'52″ = 1.79767788197 rad
Angle ∠ C = γ = 27.05221569141° = 27°3'8″ = 0.47221492079 rad

Height: ha = 13.6444042107
Height: hb = 10.72546222037
Height: hc = 22.98113332936

Median: ma = 20.22333874026
Median: mb = 12.28993939611
Median: mc = 26.05881888076

Inradius: r = 4.76107935115
Circumradius: R = 15.39113333273

Vertex coordinates: A[14; 0] B[0; 0] C[-5.28436282906; 22.98113332936]
Centroid: CG[2.90554572365; 7.66604444312]
Coordinates of the circumscribed circle: U[7; 13.70774119217]
Coordinates of the inscribed circle: I[3.79904453676; 4.76107935115]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130° = 0.8732664626 rad
∠ B' = β' = 77.05221569141° = 77°3'8″ = 1.79767788197 rad
∠ C' = γ' = 152.9487843086° = 152°56'52″ = 0.47221492079 rad

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How did we calculate this triangle?

1. Input data entered: side b, c and angle α.

b = 30 ; ; c = 14 ; ; alpha = 50° ; ;

2. Calculation of the third side a of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos alpha ; ; a = sqrt{ b**2+c**2 - 2bc cos alpha } ; ; a = sqrt{ 30**2+14**2 - 2 * 30 * 14 * cos 50° } ; ; a = 23.58 ; ;
Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 23.58 ; ; b = 30 ; ; c = 14 ; ;

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

p = a+b+c = 23.58+30+14 = 67.58 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67.58 }{ 2 } = 33.79 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.79 * (33.79-23.58)(33.79-30)(33.79-14) } ; ; T = sqrt{ 25878.94 } = 160.87 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 160.87 }{ 23.58 } = 13.64 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 160.87 }{ 30 } = 10.72 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 160.87 }{ 14 } = 22.98 ; ;

7. 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{ 30**2+14**2-23.58**2 }{ 2 * 30 * 14 } ) = 50° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 23.58**2+14**2-30**2 }{ 2 * 23.58 * 14 } ) = 102° 56'52" ; ; gamma = 180° - alpha - beta = 180° - 50° - 102° 56'52" = 27° 3'8" ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 160.87 }{ 33.79 } = 4.76 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 23.58 }{ 2 * sin 50° } = 15.39 ; ;

10. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 30**2+2 * 14**2 - 23.58**2 } }{ 2 } = 20.223 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 14**2+2 * 23.58**2 - 30**2 } }{ 2 } = 12.289 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 30**2+2 * 23.58**2 - 14**2 } }{ 2 } = 26.058 ; ;
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