Triangle calculator AAS

Please enter two angles and one opposite side
°
°


Obtuse scalene triangle.

Sides: a = 46   b = 915.6098764032   c = 948.1410630727

Area: T = 15148.57879867
Perimeter: p = 1909.749939476
Semiperimeter: s = 954.875469738

Angle ∠ A = α = 2° = 0.0354906585 rad
Angle ∠ B = β = 44° = 0.76879448709 rad
Angle ∠ C = γ = 134° = 2.33987411977 rad

Height: ha = 658.6343825507
Height: hb = 33.09896308156
Height: hc = 31.95442850411

Median: ma = 931.7332811596
Median: mb = 490.8755213904
Median: mc = 442.1376902415

Inradius: r = 15.86444668544
Circumradius: R = 659.0355292

Vertex coordinates: A[948.1410630727; 0] B[0; 0] C[33.09896308156; 31.95442850411]
Centroid: CG[327.0776753848; 10.6511428347]
Coordinates of the circumscribed circle: U[474.0770315364; -457.8044382016]
Coordinates of the inscribed circle: I[39.26659333477; 15.86444668544]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 178° = 0.0354906585 rad
∠ B' = β' = 136° = 0.76879448709 rad
∠ C' = γ' = 46° = 2.33987411977 rad

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How did we calculate this triangle?

1. Calculate the third unknown inner angle

 alpha = 2° ; ; beta = 44° ; ; ; ; alpha + beta + gamma = 180° ; ; ; ; gamma = 180° - alpha - beta = 180° - 2° - 44° = 134° ; ;

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

a = 46 ; ; ; ; fraction{ b }{ a } = fraction{ sin( beta ) }{ sin ( alpha ) } ; ; ; ; b = a * fraction{ sin( beta ) }{ sin ( alpha ) } ; ; ; ; b = 46 * fraction{ sin(44° ) }{ sin (2° ) } = 915.61 ; ;

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

 fraction{ c }{ a } = fraction{ sin( gamma ) }{ sin ( alpha ) } ; ; ; ; c = a * fraction{ sin( gamma ) }{ sin ( alpha ) } ; ; ; ; c = 46 * fraction{ sin(134° ) }{ sin (2° ) } = 948.14 ; ;


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 = 46 ; ; b = 915.61 ; ; c = 948.14 ; ;

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

p = a+b+c = 46+915.61+948.14 = 1909.75 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1909.75 }{ 2 } = 954.87 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 954.87 * (954.87-46)(954.87-915.61)(954.87-948.14) } ; ; T = sqrt{ 229479415.02 } = 15148.58 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 15148.58 }{ 46 } = 658.63 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 15148.58 }{ 915.61 } = 33.09 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 15148.58 }{ 948.14 } = 31.95 ; ;

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{ 46**2-915.61**2-948.14**2 }{ 2 * 915.61 * 948.14 } ) = 2° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 915.61**2-46**2-948.14**2 }{ 2 * 46 * 948.14 } ) = 44° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 948.14**2-46**2-915.61**2 }{ 2 * 915.61 * 46 } ) = 134° ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 15148.58 }{ 954.87 } = 15.86 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 46 }{ 2 * sin 2° } = 659.04 ; ;




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