Triangle calculator AAS

Please enter two angles and one opposite side
°
°


Obtuse scalene triangle.

Sides: a = 8.6   b = 15.5276710553   c = 18.61987979171

Area: T = 66.29551985441
Perimeter: p = 42.74655084701
Semiperimeter: s = 21.37327542351

Angle ∠ A = α = 27.3° = 27°18' = 0.47664748858 rad
Angle ∠ B = β = 55.9° = 55°54' = 0.97656390519 rad
Angle ∠ C = γ = 96.8° = 96°48' = 1.68994787159 rad

Height: ha = 15.41774880335
Height: hb = 8.54395033697
Height: hc = 7.12113188778

Median: ma = 16.59545529689
Median: mb = 12.24990870186
Median: mc = 8.41875092117

Inradius: r = 3.1021855653
Circumradius: R = 9.37553497806

Vertex coordinates: A[18.61987979171; 0] B[0; 0] C[4.82114953532; 7.12113188778]
Centroid: CG[7.81334310901; 2.37437729593]
Coordinates of the circumscribed circle: U[9.30993989586; -1.11100786183]
Coordinates of the inscribed circle: I[5.8466043682; 3.1021855653]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.7° = 152°42' = 0.47664748858 rad
∠ B' = β' = 124.1° = 124°6' = 0.97656390519 rad
∠ C' = γ' = 83.2° = 83°12' = 1.68994787159 rad

Calculate another triangle




How did we calculate this triangle?

1. Calculate the third unknown inner angle

 alpha = 27° 18' ; ; beta = 55° 54' ; ; ; ; alpha + beta + gamma = 180° ; ; ; ; gamma = 180° - alpha - beta = 180° - 27° 18' - 55° 54' = 96° 48' ; ;

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

a = 8.6 ; ; ; ; fraction{ b }{ a } = fraction{ sin( beta ) }{ sin ( alpha ) } ; ; ; ; b = a * fraction{ sin( beta ) }{ sin ( alpha ) } ; ; ; ; b = 8.6 * fraction{ sin(55° 54') }{ sin (27° 18') } = 15.53 ; ;

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 = 8.6 * fraction{ sin(96° 48') }{ sin (27° 18') } = 18.62 ; ;


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 = 8.6 ; ; b = 15.53 ; ; c = 18.62 ; ;

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

p = a+b+c = 8.6+15.53+18.62 = 42.75 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 42.75 }{ 2 } = 21.37 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21.37 * (21.37-8.6)(21.37-15.53)(21.37-18.62) } ; ; T = sqrt{ 4395.05 } = 66.3 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 66.3 }{ 8.6 } = 15.42 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 66.3 }{ 15.53 } = 8.54 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 66.3 }{ 18.62 } = 7.12 ; ;

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{ 8.6**2-15.53**2-18.62**2 }{ 2 * 15.53 * 18.62 } ) = 27° 18' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15.53**2-8.6**2-18.62**2 }{ 2 * 8.6 * 18.62 } ) = 55° 54' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18.62**2-8.6**2-15.53**2 }{ 2 * 15.53 * 8.6 } ) = 96° 48' ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 66.3 }{ 21.37 } = 3.1 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8.6 }{ 2 * sin 27° 18' } = 9.38 ; ;




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

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