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.

Acute scalene triangle.

Sides: a = 1.38224294236   b = 1.2777149604   c = 1.15108451001

Area: T = 0.68769497798
Perimeter: p = 3.81104241277
Semiperimeter: s = 1.90552120639

Angle ∠ A = α = 69.18880932308° = 69°11'17″ = 1.20875600301 rad
Angle ∠ B = β = 59.71992736979° = 59°43'9″ = 1.04222979529 rad
Angle ∠ C = γ = 51.09326330713° = 51°5'33″ = 0.89217346706 rad

Height: ha = 0.99438298015
Height: hb = 1.07657545986
Height: hc = 1.19438179687

Median: ma = 1
Median: mb = 1.1
Median: mc = 1.2

Inradius: r = 0.36105634212
Circumradius: R = 0.73994633174

Vertex coordinates: A[1.15108451001; 0] B[0; 0] C[0.69770722838; 1.19438179687]
Centroid: CG[0.61659724613; 0.39879393229]
Coordinates of the circumscribed circle: U[0.57554225501; 0.46444296358]
Coordinates of the inscribed circle: I[0.62880624598; 0.36105634212]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 110.8121906769° = 110°48'43″ = 1.20875600301 rad
∠ B' = β' = 120.2810726302° = 120°16'51″ = 1.04222979529 rad
∠ C' = γ' = 128.9077366929° = 128°54'27″ = 0.89217346706 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 = 1.1 ; ; m_c = 1.2 ; ;

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 (1.382**{ 2 } + 1.277**{ 2 }) - 4 * 1.2 **2 = 1.324 ; ; D>0 ; ; ; ; c = sqrt{ D } = sqrt{ 1.324 } = 1.151 ; ;
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 = 1.38 ; ; b = 1.28 ; ; c = 1.15 ; ;

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

p = a+b+c = 1.38+1.28+1.15 = 3.81 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 3.81 }{ 2 } = 1.91 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1.91 * (1.91-1.38)(1.91-1.28)(1.91-1.15) } ; ; T = sqrt{ 0.47 } = 0.69 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.69 }{ 1.38 } = 0.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.69 }{ 1.28 } = 1.08 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.69 }{ 1.15 } = 1.19 ; ;

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{ 1.28**2+1.15**2-1.38**2 }{ 2 * 1.28 * 1.15 } ) = 69° 11'17" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 1.38**2+1.15**2-1.28**2 }{ 2 * 1.38 * 1.15 } ) = 59° 43'9" ; ;
 gamma = 180° - alpha - beta = 180° - 69° 11'17" - 59° 43'9" = 51° 5'33" ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.69 }{ 1.91 } = 0.36 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 1.38 }{ 2 * sin 69° 11'17" } = 0.74 ; ;

10. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.28**2+2 * 1.15**2 - 1.38**2 } }{ 2 } = 1 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.15**2+2 * 1.38**2 - 1.28**2 } }{ 2 } = 1.1 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.28**2+2 * 1.38**2 - 1.15**2 } }{ 2 } = 1.2 ; ;
Calculate another triangle


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

See more information about triangles or more details on solving triangles.