Triangle calculator ASA

Please enter the side of the triangle and two adjacent angles
°
°


Obtuse scalene triangle.

Sides: a = 64.27987609687   b = 32.63551822333   c = 50

Area: T = 803.4854512108
Perimeter: p = 146.9143943202
Semiperimeter: s = 73.4576971601

Angle ∠ A = α = 100° = 1.7455329252 rad
Angle ∠ B = β = 30° = 0.52435987756 rad
Angle ∠ C = γ = 50° = 0.8732664626 rad

Height: ha = 25
Height: hb = 49.24403876506
Height: hc = 32.13993804843

Median: ma = 27.37986008003
Median: mb = 55.22333263756
Median: mc = 44.42330471212

Inradius: r = 10.93881654947
Circumradius: R = 32.63551822333

Vertex coordinates: A[50; 0] B[0; 0] C[55.66770399226; 32.13993804843]
Centroid: CG[35.22223466409; 10.71331268281]
Coordinates of the circumscribed circle: U[25; 20.97774907794]
Coordinates of the inscribed circle: I[40.82217893677; 10.93881654947]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 80° = 1.7455329252 rad
∠ B' = β' = 150° = 0.52435987756 rad
∠ C' = γ' = 130° = 0.8732664626 rad

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How did we calculate this triangle?

1. Calculate the third unknown inner angle

 alpha = 100° ; ; beta = 30° ; ; ; ; alpha + beta + gamma = 180° ; ; ; ; gamma = 180° - alpha - beta = 180° - 100° - 30° = 50° ; ;

2. By using the law of sines, we calculate unknown side a

c = 50 ; ; ; ; fraction{ a }{ c } = fraction{ sin( alpha ) }{ sin ( gamma ) } ; ; ; ; a = c * fraction{ sin( alpha ) }{ sin ( gamma ) } ; ; ; ; a = 50 * fraction{ sin(100° ) }{ sin (50° ) } = 64.28 ; ;

3. By using the law of sines, we calculate last unknown side b

 fraction{ b }{ c } = fraction{ sin( beta ) }{ sin ( gamma ) } ; ; ; ; b = c * fraction{ sin( beta ) }{ sin ( gamma ) } ; ; ; ; b = 50 * fraction{ sin(30° ) }{ sin (50° ) } = 32.64 ; ;


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 = 64.28 ; ; b = 32.64 ; ; c = 50 ; ;

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

p = a+b+c = 64.28+32.64+50 = 146.91 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 146.91 }{ 2 } = 73.46 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 73.46 * (73.46-64.28)(73.46-32.64)(73.46-50) } ; ; T = sqrt{ 645587.36 } = 803.48 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 803.48 }{ 64.28 } = 25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 803.48 }{ 32.64 } = 49.24 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 803.48 }{ 50 } = 32.14 ; ;

8. 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{ 64.28**2-32.64**2-50**2 }{ 2 * 32.64 * 50 } ) = 100° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 32.64**2-64.28**2-50**2 }{ 2 * 64.28 * 50 } ) = 30° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 50**2-64.28**2-32.64**2 }{ 2 * 32.64 * 64.28 } ) = 50° ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 803.48 }{ 73.46 } = 10.94 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 64.28 }{ 2 * sin 100° } = 32.64 ; ;




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