Triangle calculator

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

You have entered side b, c and angle α.

Obtuse scalene triangle.

Sides: a = 350.1911487603   b = 408   c = 90

Area: T = 12982.48105026
Perimeter: p = 848.1911487603
Semiperimeter: s = 424.0965743802

Angle ∠ A = α = 45° = 0.78553981634 rad
Angle ∠ B = β = 124.5329570942° = 124°31'46″ = 2.1733451029 rad
Angle ∠ C = γ = 10.47704290582° = 10°28'14″ = 0.18327434612 rad

Height: ha = 74.14550375704
Height: hb = 63.64396103068
Height: hc = 288.5499566724

Median: ma = 237.9576887907
Median: mb = 154.1143720982
Median: mc = 377.5243560847

Inradius: r = 30.61221452345
Circumradius: R = 247.6232775598

Vertex coordinates: A[90; 0] B[0; 0] C[-198.5499566724; 288.5499566724]
Centroid: CG[-36.16765222414; 96.16765222414]
Coordinates of the circumscribed circle: U[45; 243.5499566724]
Coordinates of the inscribed circle: I[16.09657438015; 30.61221452345]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135° = 0.78553981634 rad
∠ B' = β' = 55.47704290582° = 55°28'14″ = 2.1733451029 rad
∠ C' = γ' = 169.5329570942° = 169°31'46″ = 0.18327434612 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 = 350.19 ; ; b = 408 ; ; c = 90 ; ;

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

p = a+b+c = 350.19+408+90 = 848.19 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 848.19 }{ 2 } = 424.1 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 424.1 * (424.1-350.19)(424.1-408)(424.1-90) } ; ; T = sqrt{ 168544800 } = 12982.48 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 12982.48 }{ 350.19 } = 74.15 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 12982.48 }{ 408 } = 63.64 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 12982.48 }{ 90 } = 288.5 ; ;

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{ 350.19**2-408**2-90**2 }{ 2 * 408 * 90 } ) = 45° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 408**2-350.19**2-90**2 }{ 2 * 350.19 * 90 } ) = 124° 31'46" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 90**2-350.19**2-408**2 }{ 2 * 408 * 350.19 } ) = 10° 28'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 12982.48 }{ 424.1 } = 30.61 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 350.19 }{ 2 * sin 45° } = 247.62 ; ;




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

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