Triangle calculator

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

You have entered side b, c and angle α.

Right scalene triangle.

Sides: a = 1180.042237212   b = 700   c = 950

Area: T = 332500
Perimeter: p = 2830.042237212
Semiperimeter: s = 1415.021118606

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 36.38443518158° = 36°23'4″ = 0.63550267354 rad
Angle ∠ C = γ = 53.61656481842° = 53°36'56″ = 0.93657695914 rad

Height: ha = 563.5399086147
Height: hb = 950
Height: hc = 700

Median: ma = 590.021118606
Median: mb = 1012.423283657
Median: mc = 845.9466215784

Inradius: r = 234.979881394
Circumradius: R = 590.021118606

Vertex coordinates: A[950; 0] B[0; 0] C[950; 700]
Centroid: CG[633.3333333333; 233.3333333333]
Coordinates of the circumscribed circle: U[475; 350]
Coordinates of the inscribed circle: I[715.021118606; 234.979881394]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 143.6165648184° = 143°36'56″ = 0.63550267354 rad
∠ C' = γ' = 126.3844351816° = 126°23'4″ = 0.93657695914 rad

Calculate another triangle




How did we calculate this triangle?

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

b = 700 ; ; c = 950 ; ; alpha = 90° ; ;

2. Calculation of the third side a of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos alpha ; ; a = sqrt{ b**2+c**2 - 2bc cos alpha } ; ; a = sqrt{ 700**2+950**2 - 2 * 700 * 950 * cos(90° ) } ; ; a = 1180.04 ; ;


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 = 1180.04 ; ; b = 700 ; ; c = 950 ; ;

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

p = a+b+c = 1180.04+700+950 = 2830.04 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 2830.04 }{ 2 } = 1415.02 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1415.02 * (1415.02-1180.04)(1415.02-700)(1415.02-950) } ; ; T = sqrt{ 110556250000 } = 332500 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 332500 }{ 1180.04 } = 563.54 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 332500 }{ 700 } = 950 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 332500 }{ 950 } = 700 ; ;

7. 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{ 1180.04**2-700**2-950**2 }{ 2 * 700 * 950 } ) = 90° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 700**2-1180.04**2-950**2 }{ 2 * 1180.04 * 950 } ) = 36° 23'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 950**2-1180.04**2-700**2 }{ 2 * 700 * 1180.04 } ) = 53° 36'56" ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 332500 }{ 1415.02 } = 234.98 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1180.04 }{ 2 * sin 90° } = 590.02 ; ;




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

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