Triangle calculator

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 = 7.42436858171   b = 9.04331066442   c = 4.21663702136

Area: T = 15.49219333848
Perimeter: p = 20.68331626748
Semiperimeter: s = 10.34215813374

Angle ∠ A = α = 54.3511185088° = 54°21'4″ = 0.94986071321 rad
Angle ∠ B = β = 98.16330419156° = 98°9'47″ = 1.71332682852 rad
Angle ∠ C = γ = 27.48657729965° = 27°29'9″ = 0.48797172362 rad

Height: ha = 4.17436500618
Height: hb = 3.42662414443
Height: hc = 7.34884692283

Median: ma = 6
Median: mb = 4
Median: mc = 8

Inradius: r = 1.49880236464
Circumradius: R = 4.56878345007

Vertex coordinates: A[4.21663702136; 0] B[0; 0] C[-1.05440925534; 7.34884692283]
Centroid: CG[1.05440925534; 2.44994897428]
Coordinates of the circumscribed circle: U[2.10881851068; 4.05222422905]
Coordinates of the inscribed circle: I[1.29884746932; 1.49880236464]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.6498814912° = 125°38'56″ = 0.94986071321 rad
∠ B' = β' = 81.83769580844° = 81°50'13″ = 1.71332682852 rad
∠ C' = γ' = 152.5144227004° = 152°30'51″ = 0.48797172362 rad

Calculate another triangle




How did we calculate this triangle?

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

m_a = 6 ; ; m_b = 4 ; ; m_c = 8 ; ;

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 (7.424**{ 2 } + 9.043**{ 2 }) - 4 * 8 **2 = 17.778 ; ; D>0 ; ; ; ; c = sqrt{ D } = sqrt{ 17.778 } = 4.216 ; ;
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 = 7.42 ; ; b = 9.04 ; ; c = 4.22 ; ;

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

p = a+b+c = 7.42+9.04+4.22 = 20.68 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 20.68 }{ 2 } = 10.34 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 10.34 * (10.34-7.42)(10.34-9.04)(10.34-4.22) } ; ; T = sqrt{ 240 } = 15.49 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 15.49 }{ 7.42 } = 4.17 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 15.49 }{ 9.04 } = 3.43 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 15.49 }{ 4.22 } = 7.35 ; ;

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{ 9.04**2+4.22**2-7.42**2 }{ 2 * 9.04 * 4.22 } ) = 54° 21'4" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 7.42**2+4.22**2-9.04**2 }{ 2 * 7.42 * 4.22 } ) = 98° 9'47" ; ; gamma = 180° - alpha - beta = 180° - 54° 21'4" - 98° 9'47" = 27° 29'9" ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 15.49 }{ 10.34 } = 1.5 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 7.42 }{ 2 * sin 54° 21'4" } = 4.57 ; ;

10. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.04**2+2 * 4.22**2 - 7.42**2 } }{ 2 } = 6 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.22**2+2 * 7.42**2 - 9.04**2 } }{ 2 } = 4 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.04**2+2 * 7.42**2 - 4.22**2 } }{ 2 } = 8 ; ;
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.