Triangle calculator

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

You have entered side b, angle α and angle β.

Right scalene triangle.

Sides: a = 439.8387904317   b = 1286   c = 1208.445471033

Area: T = 265759.8944437
Perimeter: p = 2934.283261465
Semiperimeter: s = 1467.141130732

Angle ∠ A = α = 20° = 0.34990658504 rad
Angle ∠ B = β = 90° = 1.57107963268 rad
Angle ∠ C = γ = 70° = 1.22217304764 rad

Height: ha = 1208.445471033
Height: hb = 413.3122433028
Height: hc = 439.8387904317

Median: ma = 1228.293270268
Median: mb = 643
Median: mc = 747.3576699679

Inradius: r = 181.1411307324
Circumradius: R = 643

Vertex coordinates: A[1208.445471033; 0] B[0; 0] C[-0; 439.8387904317]
Centroid: CG[402.8154903444; 146.6132634772]
Coordinates of the circumscribed circle: U[604.2222355165; 219.9198952158]
Coordinates of the inscribed circle: I[181.1411307324; 181.1411307324]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160° = 0.34990658504 rad
∠ B' = β' = 90° = 1.57107963268 rad
∠ C' = γ' = 110° = 1.22217304764 rad

Calculate another triangle




How did we calculate this triangle?

1. Input data entered: side b, angle α and angle β.

b = 1286 ; ; alpha = 20° ; ; beta = 90° ; ;

2. From angle α and angle β we calculate γ:

 alpha + beta + gamma = 180° ; ; gamma = 180° - alpha - beta = 180° - 20 ° - 90 ° = 70 ° ; ;

3. From angle α, angle β and side b we calculate a - By using the law of sines, we calculate unknown side a:

 fraction{ a }{ b } = fraction{ sin( alpha ) }{ sin ( beta ) } ; ; ; ; a = b * fraction{ sin( alpha ) }{ sin ( beta ) } ; ; ; ; a = 1286 * fraction{ sin(20° ) }{ sin (90° ) } = 439.84 ; ;

4. Calculation of the third side c of the triangle using a Law of Cosines

c**2 = b**2+a**2 - 2ba cos gamma ; ; c = sqrt{ b**2+a**2 - 2ba cos gamma } ; ; c = sqrt{ 1286**2+439.84**2 - 2 * 1286 * 439.84 * cos(70° ) } ; ; c = 1208.44 ; ;


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 = 439.84 ; ; b = 1286 ; ; c = 1208.44 ; ;

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

p = a+b+c = 439.84+1286+1208.44 = 2934.28 ; ;

6. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 2934.28 }{ 2 } = 1467.14 ; ;

7. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1467.14 * (1467.14-439.84)(1467.14-1286)(1467.14-1208.44) } ; ; T = sqrt{ 70628321491.3 } = 265759.89 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 265759.89 }{ 439.84 } = 1208.44 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 265759.89 }{ 1286 } = 413.31 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 265759.89 }{ 1208.44 } = 439.84 ; ;

9. 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{ 439.84**2-1286**2-1208.44**2 }{ 2 * 1286 * 1208.44 } ) = 20° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 1286**2-439.84**2-1208.44**2 }{ 2 * 439.84 * 1208.44 } ) = 90° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 1208.44**2-439.84**2-1286**2 }{ 2 * 1286 * 439.84 } ) = 70° ; ;

10. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 265759.89 }{ 1467.14 } = 181.14 ; ;

11. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 439.84 }{ 2 * sin 20° } = 643 ; ;




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

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