Triangle calculator

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

You have entered side a, b and c.

Obtuse scalene triangle.

Sides: a = 14.9   b = 23.8   c = 36.9

Area: T = 104.4365683557
Perimeter: p = 75.6
Semiperimeter: s = 37.8

Angle ∠ A = α = 13.75987896448° = 13°45'32″ = 0.24401361804 rad
Angle ∠ B = β = 22.32773250026° = 22°19'38″ = 0.39896853345 rad
Angle ∠ C = γ = 143.9143885353° = 143°54'50″ = 2.51217711387 rad

Height: ha = 14.0188212558
Height: hb = 8.77661078619
Height: hc = 5.66604706535

Median: ma = 30.14217069855
Median: mb = 25.4999019589
Median: mc = 7.33663819421

Inradius: r = 2.76328487713
Circumradius: R = 31.32442503767

Vertex coordinates: A[36.9; 0] B[0; 0] C[13.78329268293; 5.66604706535]
Centroid: CG[16.89443089431; 1.88768235512]
Coordinates of the circumscribed circle: U[18.45; -25.31441494359]
Coordinates of the inscribed circle: I[14; 2.76328487713]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.2411210355° = 166°14'28″ = 0.24401361804 rad
∠ B' = β' = 157.6732674997° = 157°40'22″ = 0.39896853345 rad
∠ C' = γ' = 36.08661146473° = 36°5'10″ = 2.51217711387 rad

Calculate another triangle




How did we calculate this triangle?

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 = 14.9 ; ; b = 23.8 ; ; c = 36.9 ; ;

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

p = a+b+c = 14.9+23.8+36.9 = 75.6 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 75.6 }{ 2 } = 37.8 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37.8 * (37.8-14.9)(37.8-23.8)(37.8-36.9) } ; ; T = sqrt{ 10906.81 } = 104.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 104.44 }{ 14.9 } = 14.02 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 104.44 }{ 23.8 } = 8.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 104.44 }{ 36.9 } = 5.66 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 14.9**2-23.8**2-36.9**2 }{ 2 * 23.8 * 36.9 } ) = 13° 45'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23.8**2-14.9**2-36.9**2 }{ 2 * 14.9 * 36.9 } ) = 22° 19'38" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 36.9**2-14.9**2-23.8**2 }{ 2 * 23.8 * 14.9 } ) = 143° 54'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 104.44 }{ 37.8 } = 2.76 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14.9 }{ 2 * sin 13° 45'32" } = 31.32 ; ;




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

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