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 = 1040.625481231   b = 350   c = 980

Area: T = 171500
Perimeter: p = 2370.625481231
Semiperimeter: s = 1185.312240616

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 19.65438240581° = 19°39'14″ = 0.34330239404 rad
Angle ∠ C = γ = 70.34661759419° = 70°20'46″ = 1.22877723864 rad

Height: ha = 329.6109669058
Height: hb = 980
Height: hc = 350

Median: ma = 520.3122406156
Median: mb = 995.5022385733
Median: mc = 602.1632768693

Inradius: r = 144.6887593844
Circumradius: R = 520.3122406156

Vertex coordinates: A[980; 0] B[0; 0] C[980; 350]
Centroid: CG[653.3333333333; 116.6676666667]
Coordinates of the circumscribed circle: U[490; 175]
Coordinates of the inscribed circle: I[835.3122406156; 144.6887593844]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 160.3466175942° = 160°20'46″ = 0.34330239404 rad
∠ C' = γ' = 109.6543824058° = 109°39'14″ = 1.22877723864 rad

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How did we calculate this triangle?

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

b = 350 ; ; c = 980 ; ; 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{ 350**2+980**2 - 2 * 350 * 980 * cos(90° ) } ; ; a = 1040.62 ; ;


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 = 1040.62 ; ; b = 350 ; ; c = 980 ; ;

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

p = a+b+c = 1040.62+350+980 = 2370.62 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 2370.62 }{ 2 } = 1185.31 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1185.31 * (1185.31-1040.62)(1185.31-350)(1185.31-980) } ; ; T = sqrt{ 29412250000 } = 171500 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 171500 }{ 1040.62 } = 329.61 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 171500 }{ 350 } = 980 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 171500 }{ 980 } = 350 ; ;

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{ 1040.62**2-350**2-980**2 }{ 2 * 350 * 980 } ) = 90° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 350**2-1040.62**2-980**2 }{ 2 * 1040.62 * 980 } ) = 19° 39'14" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 980**2-1040.62**2-350**2 }{ 2 * 350 * 1040.62 } ) = 70° 20'46" ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 171500 }{ 1185.31 } = 144.69 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1040.62 }{ 2 * sin 90° } = 520.31 ; ;




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