Triangle calculator ASA

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


Right scalene triangle.

Sides: a = 99.38765133194   b = 25.72331224734   c = 96

Area: T = 1234.710987872
Perimeter: p = 221.1109635793
Semiperimeter: s = 110.5554817896

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 15° = 0.26217993878 rad
Angle ∠ C = γ = 75° = 1.3098996939 rad

Height: ha = 24.84766283298
Height: hb = 96
Height: hc = 25.72331224734

Median: ma = 49.69332566597
Median: mb = 96.85877294667
Median: mc = 54.45880483472

Inradius: r = 11.1688304577
Circumradius: R = 49.69332566597

Vertex coordinates: A[96; 0] B[0; 0] C[96; 25.72331224734]
Centroid: CG[64; 8.57443741578]
Coordinates of the circumscribed circle: U[48; 12.86215612367]
Coordinates of the inscribed circle: I[84.8321695423; 11.1688304577]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 165° = 0.26217993878 rad
∠ C' = γ' = 105° = 1.3098996939 rad

Calculate another triangle




How did we calculate this triangle?

1. Calculate the third unknown inner angle

 alpha = 90° ; ; beta = 15° ; ; ; ; alpha + beta + gamma = 180° ; ; ; ; gamma = 180° - alpha - beta = 180° - 90° - 15° = 75° ; ;

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

c = 96 ; ; ; ; fraction{ a }{ c } = fraction{ sin( alpha ) }{ sin ( gamma ) } ; ; ; ; a = c * fraction{ sin( alpha ) }{ sin ( gamma ) } ; ; ; ; a = 96 * fraction{ sin(90° ) }{ sin (75° ) } = 99.39 ; ;

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 = 96 * fraction{ sin(15° ) }{ sin (75° ) } = 25.72 ; ;


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 = 99.39 ; ; b = 25.72 ; ; c = 96 ; ;

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

p = a+b+c = 99.39+25.72+96 = 221.11 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 221.11 }{ 2 } = 110.55 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 110.55 * (110.55-99.39)(110.55-25.72)(110.55-96) } ; ; T = sqrt{ 1524508.48 } = 1234.71 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1234.71 }{ 99.39 } = 24.85 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1234.71 }{ 25.72 } = 96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1234.71 }{ 96 } = 25.72 ; ;

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{ 99.39**2-25.72**2-96**2 }{ 2 * 25.72 * 96 } ) = 90° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25.72**2-99.39**2-96**2 }{ 2 * 99.39 * 96 } ) = 15° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 96**2-99.39**2-25.72**2 }{ 2 * 25.72 * 99.39 } ) = 75° ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1234.71 }{ 110.55 } = 11.17 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 99.39 }{ 2 * sin 90° } = 49.69 ; ;




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

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