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 = 2.7   b = 1.8   c = 3.6

Area: T = 2.35328373828
Perimeter: p = 8.1
Semiperimeter: s = 4.05

Angle ∠ A = α = 46.56774634422° = 46°34'3″ = 0.81327555614 rad
Angle ∠ B = β = 28.95550243719° = 28°57'18″ = 0.50553605103 rad
Angle ∠ C = γ = 104.4787512186° = 104°28'39″ = 1.82334765819 rad

Height: ha = 1.74328425058
Height: hb = 2.61442637587
Height: hc = 1.30771318793

Median: ma = 2.50554939633
Median: mb = 3.05220484924
Median: mc = 1.42330249471

Inradius: r = 0.58109475019
Circumradius: R = 1.85990320062

Vertex coordinates: A[3.6; 0] B[0; 0] C[2.36325; 1.30771318793]
Centroid: CG[1.98875; 0.43657106264]
Coordinates of the circumscribed circle: U[1.8; -0.46547580015]
Coordinates of the inscribed circle: I[2.25; 0.58109475019]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 133.4332536558° = 133°25'57″ = 0.81327555614 rad
∠ B' = β' = 151.0454975628° = 151°2'42″ = 0.50553605103 rad
∠ C' = γ' = 75.52224878141° = 75°31'21″ = 1.82334765819 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 = 2.7 ; ; b = 1.8 ; ; c = 3.6 ; ;

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

p = a+b+c = 2.7+1.8+3.6 = 8.1 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 8.1 }{ 2 } = 4.05 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 4.05 * (4.05-2.7)(4.05-1.8)(4.05-3.6) } ; ; T = sqrt{ 5.54 } = 2.35 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2.35 }{ 2.7 } = 1.74 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2.35 }{ 1.8 } = 2.61 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2.35 }{ 3.6 } = 1.31 ; ;

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{ 2.7**2-1.8**2-3.6**2 }{ 2 * 1.8 * 3.6 } ) = 46° 34'3" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 1.8**2-2.7**2-3.6**2 }{ 2 * 2.7 * 3.6 } ) = 28° 57'18" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 3.6**2-2.7**2-1.8**2 }{ 2 * 1.8 * 2.7 } ) = 104° 28'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2.35 }{ 4.05 } = 0.58 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2.7 }{ 2 * sin 46° 34'3" } = 1.86 ; ;




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

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