Triangle calculator

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

You have entered side a, b and angle α.

Obtuse scalene triangle.

Sides: a = 100   b = 90   c = 168.6954510132

Area: T = 3680.312246275
Perimeter: p = 358.6954510132
Semiperimeter: s = 179.3477255066

Angle ∠ A = α = 29° = 0.50661454831 rad
Angle ∠ B = β = 25.8769868638° = 25°52'12″ = 0.45215143848 rad
Angle ∠ C = γ = 125.1330131362° = 125°7'48″ = 2.18439327857 rad

Height: ha = 73.6066249255
Height: hb = 81.78547213945
Height: hc = 43.63328658222

Median: ma = 125.6144166694
Median: mb = 131.1643710203
Median: mc = 43.99547788138

Inradius: r = 20.52105954304
Circumradius: R = 103.1333266981

Vertex coordinates: A[168.6954510132; 0] B[0; 0] C[89.97987364889; 43.63328658222]
Centroid: CG[86.22444155401; 14.54442886074]
Coordinates of the circumscribed circle: U[84.34772550657; -59.34765358814]
Coordinates of the inscribed circle: I[89.34772550657; 20.52105954304]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151° = 0.50661454831 rad
∠ B' = β' = 154.1330131362° = 154°7'48″ = 0.45215143848 rad
∠ C' = γ' = 54.8769868638° = 54°52'12″ = 2.18439327857 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 = 100 ; ; b = 90 ; ; c = 168.69 ; ;

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

p = a+b+c = 100+90+168.69 = 358.69 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 358.69 }{ 2 } = 179.35 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 179.35 * (179.35-100)(179.35-90)(179.35-168.69) } ; ; T = sqrt{ 13544699.82 } = 3680.31 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3680.31 }{ 100 } = 73.61 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3680.31 }{ 90 } = 81.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3680.31 }{ 168.69 } = 43.63 ; ;

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{ 100**2-90**2-168.69**2 }{ 2 * 90 * 168.69 } ) = 29° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 90**2-100**2-168.69**2 }{ 2 * 100 * 168.69 } ) = 25° 52'12" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 168.69**2-100**2-90**2 }{ 2 * 90 * 100 } ) = 125° 7'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3680.31 }{ 179.35 } = 20.52 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 100 }{ 2 * sin 29° } = 103.13 ; ;




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

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