Triangle calculator

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

You have entered side a, b and angle γ.

Obtuse scalene triangle.

Sides: a = 0.03   b = 0.33   c = 0.312156509

Area: T = 0.004379192
Perimeter: p = 0.672156509
Semiperimeter: s = 0.3365782545

Angle ∠ A = α = 4.23300320762° = 4°13'48″ = 0.07438279872 rad
Angle ∠ B = β = 125.7769967924° = 125°46'12″ = 2.19551000404 rad
Angle ∠ C = γ = 50° = 0.8732664626 rad

Height: ha = 0.25327946662
Height: hb = 0.02329813333
Height: hc = 0.02443411095

Median: ma = 0.32105641943
Median: mb = 0.14875174656
Median: mc = 0.17550194237

Inradius: r = 0.01112927847
Circumradius: R = 0.20333596698

Vertex coordinates: A[0.312156509; 0] B[0; 0] C[-0.01875359741; 0.02443411095]
Centroid: CG[0.09880097053; 0.00881137032]
Coordinates of the circumscribed circle: U[0.1565782545; 0.13107170761]
Coordinates of the inscribed circle: I[0.0065782545; 0.01112927847]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 175.7769967924° = 175°46'12″ = 0.07438279872 rad
∠ B' = β' = 54.23300320762° = 54°13'48″ = 2.19551000404 rad
∠ C' = γ' = 130° = 0.8732664626 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 = 0.03 ; ; b = 0.33 ; ; c = 0.31 ; ;

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

p = a+b+c = 0.03+0.33+0.31 = 0.67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 0.67 }{ 2 } = 0.34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 0.34 * (0.34-0.03)(0.34-0.33)(0.34-0.31) } ; ; T = sqrt{ 0 } = 0 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0 }{ 0.03 } = 0.25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0 }{ 0.33 } = 0.02 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0 }{ 0.31 } = 0.02 ; ;

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{ 0.03**2-0.33**2-0.31**2 }{ 2 * 0.33 * 0.31 } ) = 4° 13'48" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 0.33**2-0.03**2-0.31**2 }{ 2 * 0.03 * 0.31 } ) = 125° 46'12" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 0.31**2-0.03**2-0.33**2 }{ 2 * 0.33 * 0.03 } ) = 50° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0 }{ 0.34 } = 0.01 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 0.03 }{ 2 * sin 4° 13'48" } = 0.2 ; ;




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

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