Triangle calculator - result

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

You have entered median ma, median mb and median mc.

Obtuse scalene triangle.

Sides: a = 2.94439202888   b = 1.29109944487   c = 2.16602468995

Area: T = 1.26765570128
Perimeter: p = 6.3955161637
Semiperimeter: s = 3.19875808185

Angle ∠ A = α = 114.7299199063° = 114°43'45″ = 2.00224022718 rad
Angle ∠ B = β = 23.47328053046° = 23°28'22″ = 0.41096777372 rad
Angle ∠ C = γ = 41.79879956322° = 41°47'53″ = 0.73295126445 rad

Height: ha = 0.86604560508
Height: hb = 1.9622141687
Height: hc = 1.173260394

Median: ma = 1
Median: mb = 2.5
Median: mc = 2

Inradius: r = 0.39660985147
Circumradius: R = 1.62105747827

Vertex coordinates: A[2.16602468995; 0] B[0; 0] C[2.77003086243; 1.173260394]
Centroid: CG[1.62201851746; 0.391086798]
Coordinates of the circumscribed circle: U[1.08801234497; 1.20881373927]
Coordinates of the inscribed circle: I[1.90765863698; 0.39660985147]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 65.27108009368° = 65°16'15″ = 2.00224022718 rad
∠ B' = β' = 156.5277194695° = 156°31'38″ = 0.41096777372 rad
∠ C' = γ' = 138.2022004368° = 138°12'7″ = 0.73295126445 rad

Calculate another triangle




How did we calculate this triangle?

1. Input data entered: median ma, median mb and median mc.

m_a = 1 ; ; m_b = 2.5 ; ; m_c = 2 ; ;

2. From side a, side b and median mc we calculate side c:

D = 2 (a**{ 2 } + b**{ 2 }) - 4 * m_c **2 ; ; D = 2 (2.944**{ 2 } + 1.291**{ 2 }) - 4 * 2 **2 = 4.667 ; ; D>0 ; ; ; ; c = sqrt{ D } = sqrt{ 4.667 } = 2.16 ; ;
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 = 2.94 ; ; b = 1.29 ; ; c = 2.16 ; ;

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

p = a+b+c = 2.94+1.29+2.16 = 6.4 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 6.4 }{ 2 } = 3.2 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 3.2 * (3.2-2.94)(3.2-1.29)(3.2-2.16) } ; ; T = sqrt{ 1.6 } = 1.27 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.27 }{ 2.94 } = 0.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.27 }{ 1.29 } = 1.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.27 }{ 2.16 } = 1.17 ; ;

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{ 1.29**2+2.16**2-2.94**2 }{ 2 * 1.29 * 2.16 } ) = 114° 43'45" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 2.94**2+2.16**2-1.29**2 }{ 2 * 2.94 * 2.16 } ) = 23° 28'22" ; ; gamma = 180° - alpha - beta = 180° - 114° 43'45" - 23° 28'22" = 41° 47'53" ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.27 }{ 3.2 } = 0.4 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 2.94 }{ 2 * sin 114° 43'45" } = 1.62 ; ;

10. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.29**2+2 * 2.16**2 - 2.94**2 } }{ 2 } = 1 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.16**2+2 * 2.94**2 - 1.29**2 } }{ 2 } = 2.5 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.29**2+2 * 2.94**2 - 2.16**2 } }{ 2 } = 2 ; ;
Calculate another triangle

Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.