Triangle calculator

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

You have entered side a, b and c.

Acute scalene triangle.

Sides: a = 150   b = 340   c = 369

Area: T = 25495.39220824
Perimeter: p = 859
Semiperimeter: s = 429.5

Angle ∠ A = α = 23.98108075536° = 23°58'51″ = 0.41985440491 rad
Angle ∠ B = β = 67.10884395912° = 67°6'30″ = 1.17112632267 rad
Angle ∠ C = γ = 88.91107528552° = 88°54'39″ = 1.55217853777 rad

Height: ha = 339.9398561099
Height: hb = 149.9732894603
Height: hc = 138.1866406951

Median: ma = 346.7798747907
Median: mb = 224.5677361832
Median: mc = 187.1098925495

Inradius: r = 59.36106334865
Circumradius: R = 184.5333345664

Vertex coordinates: A[369; 0] B[0; 0] C[58.34882384824; 138.1866406951]
Centroid: CG[142.4499412827; 46.06221356503]
Coordinates of the circumscribed circle: U[184.5; 3.50879427181]
Coordinates of the inscribed circle: I[89.5; 59.36106334865]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.0199192446° = 156°1'9″ = 0.41985440491 rad
∠ B' = β' = 112.8921560409° = 112°53'30″ = 1.17112632267 rad
∠ C' = γ' = 91.08992471448° = 91°5'21″ = 1.55217853777 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 = 150 ; ; b = 340 ; ; c = 369 ; ;

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

p = a+b+c = 150+340+369 = 859 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 859 }{ 2 } = 429.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 429.5 * (429.5-150)(429.5-340)(429.5-369) } ; ; T = sqrt{ 650015017.44 } = 25495.39 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 25495.39 }{ 150 } = 339.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 25495.39 }{ 340 } = 149.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 25495.39 }{ 369 } = 138.19 ; ;

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{ 150**2-340**2-369**2 }{ 2 * 340 * 369 } ) = 23° 58'51" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 340**2-150**2-369**2 }{ 2 * 150 * 369 } ) = 67° 6'30" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 369**2-150**2-340**2 }{ 2 * 340 * 150 } ) = 88° 54'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 25495.39 }{ 429.5 } = 59.36 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 150 }{ 2 * sin 23° 58'51" } = 184.53 ; ;




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

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