Triangle calculator AAS

Please enter two angles and one opposite side
°
°


Right scalene triangle.

Sides: a = 256   b = 221.7032503369   c = 128

Area: T = 14188.96602156
Perimeter: p = 605.7032503369
Semiperimeter: s = 302.8511251684

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 60° = 1.04771975512 rad
Angle ∠ C = γ = 30° = 0.52435987756 rad

Height: ha = 110.8511251684
Height: hb = 128
Height: hc = 221.7032503369

Median: ma = 128
Median: mb = 169.3288083908
Median: mc = 230.755528163

Inradius: r = 46.85112516844
Circumradius: R = 128

Vertex coordinates: A[128; 0] B[0; 0] C[128; 221.7032503369]
Centroid: CG[85.33333333333; 73.90108344563]
Coordinates of the circumscribed circle: U[64; 110.8511251684]
Coordinates of the inscribed circle: I[81.14987483156; 46.85112516844]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 120° = 1.04771975512 rad
∠ C' = γ' = 150° = 0.52435987756 rad

Calculate another triangle




How did we calculate this triangle?

1. Calculate the third unknown inner angle

 alpha = 90° ; ; beta = 60° ; ; ; ; alpha + beta + gamma = 180° ; ; ; ; gamma = 180° - alpha - beta = 180° - 90° - 60° = 30° ; ;

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

a = 256 ; ; ; ; fraction{ b }{ a } = fraction{ sin( beta ) }{ sin ( alpha ) } ; ; ; ; b = a * fraction{ sin( beta ) }{ sin ( alpha ) } ; ; ; ; b = 256 * fraction{ sin(60° ) }{ sin (90° ) } = 221.7 ; ;

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 = 256 * fraction{ sin(30° ) }{ sin (90° ) } = 128 ; ;


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 = 256 ; ; b = 221.7 ; ; c = 128 ; ;

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

p = a+b+c = 256+221.7+128 = 605.7 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 605.7 }{ 2 } = 302.85 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 302.85 * (302.85-256)(302.85-221.7)(302.85-128) } ; ; T = sqrt{ 201326592 } = 14188.96 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 14188.96 }{ 256 } = 110.85 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 14188.96 }{ 221.7 } = 128 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 14188.96 }{ 128 } = 221.7 ; ;

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{ 256**2-221.7**2-128**2 }{ 2 * 221.7 * 128 } ) = 90° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 221.7**2-256**2-128**2 }{ 2 * 256 * 128 } ) = 60° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 128**2-256**2-221.7**2 }{ 2 * 221.7 * 256 } ) = 30° ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 14188.96 }{ 302.85 } = 46.85 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 256 }{ 2 * sin 90° } = 128 ; ;




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

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