Triangle calculator ASA

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


Right scalene triangle.

Sides: a = 24.2498711306   b = 48.49774226119   c = 42

Area: T = 509.2232937425
Perimeter: p = 114.7466133918
Semiperimeter: s = 57.37330669589

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

Height: ha = 42
Height: hb = 21
Height: hc = 24.2498711306

Median: ma = 43.71549859888
Median: mb = 24.2498711306
Median: mc = 32.07880298647

Inradius: r = 8.8765644347
Circumradius: R = 24.2498711306

Vertex coordinates: A[42; 0] B[0; 0] C[-0; 24.2498711306]
Centroid: CG[14; 8.08329037687]
Coordinates of the circumscribed circle: U[21; 12.1244355653]
Coordinates of the inscribed circle: I[8.8765644347; 8.8765644347]

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

Calculate another triangle




How did we calculate this triangle?

1. Calculate the third unknown inner angle

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

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

c = 42 ; ; ; ; fraction{ a }{ c } = fraction{ sin( alpha ) }{ sin ( gamma ) } ; ; ; ; a = c * fraction{ sin( alpha ) }{ sin ( gamma ) } ; ; ; ; a = 42 * fraction{ sin(30° ) }{ sin (60° ) } = 24.25 ; ;

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 = 42 * fraction{ sin(90° ) }{ sin (60° ) } = 48.5 ; ;


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 = 24.25 ; ; b = 48.5 ; ; c = 42 ; ;

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

p = a+b+c = 24.25+48.5+42 = 114.75 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 114.75 }{ 2 } = 57.37 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 57.37 * (57.37-24.25)(57.37-48.5)(57.37-42) } ; ; T = sqrt{ 259308 } = 509.22 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 509.22 }{ 24.25 } = 42 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 509.22 }{ 48.5 } = 21 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 509.22 }{ 42 } = 24.25 ; ;

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{ 24.25**2-48.5**2-42**2 }{ 2 * 48.5 * 42 } ) = 30° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 48.5**2-24.25**2-42**2 }{ 2 * 24.25 * 42 } ) = 90° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 42**2-24.25**2-48.5**2 }{ 2 * 48.5 * 24.25 } ) = 60° ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 509.22 }{ 57.37 } = 8.88 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 24.25 }{ 2 * sin 30° } = 24.25 ; ;




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

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