Triangle calculator ASA

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


Obtuse scalene triangle.

Sides: a = 13.32550975438   b = 25.8770061167   c = 29.75

Area: T = 172.0955158236
Perimeter: p = 68.94551587108
Semiperimeter: s = 34.47325793554

Angle ∠ A = α = 26.565° = 26°33'54″ = 0.46436467158 rad
Angle ∠ B = β = 60.25551° = 60°15'18″ = 1.05216498861 rad
Angle ∠ C = γ = 93.18799° = 93°10'48″ = 1.62662960517 rad

Height: ha = 25.83302286601
Height: hb = 13.30545806985
Height: hc = 11.56994224025

Median: ma = 27.07697566715
Median: mb = 19.07986620621
Median: mc = 14.21877185114

Inradius: r = 4.99222332896
Circumradius: R = 14.89879385713

Vertex coordinates: A[29.75; 0] B[0; 0] C[6.61111035255; 11.56994224025]
Centroid: CG[12.12203678418; 3.85664741342]
Coordinates of the circumscribed circle: U[14.875; -0.8266407087]
Coordinates of the inscribed circle: I[8.60325181884; 4.99222332896]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.435° = 153°26'6″ = 0.46436467158 rad
∠ B' = β' = 119.74549° = 119°44'42″ = 1.05216498861 rad
∠ C' = γ' = 86.82201° = 86°49'12″ = 1.62662960517 rad

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How did we calculate this triangle?

1. Calculate the third unknown inner angle

 alpha = 26° 33'54" ; ; beta = 60° 15'18" ; ; ; ; alpha + beta + gamma = 180° ; ; ; ; gamma = 180° - alpha - beta = 180° - 26° 33'54" - 60° 15'18" = 93° 10'48" ; ;

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

c = 29.75 ; ; ; ; fraction{ a }{ c } = fraction{ sin( alpha ) }{ sin ( gamma ) } ; ; ; ; a = c * fraction{ sin( alpha ) }{ sin ( gamma ) } ; ; ; ; a = 29.75 * fraction{ sin(26° 33'54") }{ sin (93° 10'48") } = 13.33 ; ;

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 = 29.75 * fraction{ sin(60° 15'18") }{ sin (93° 10'48") } = 25.87 ; ;


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 = 13.33 ; ; b = 25.87 ; ; c = 29.75 ; ;

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

p = a+b+c = 13.33+25.87+29.75 = 68.95 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 68.95 }{ 2 } = 34.47 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34.47 * (34.47-13.33)(34.47-25.87)(34.47-29.75) } ; ; T = sqrt{ 29616.74 } = 172.1 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 172.1 }{ 13.33 } = 25.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 172.1 }{ 25.87 } = 13.3 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 172.1 }{ 29.75 } = 11.57 ; ;

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{ 13.33**2-25.87**2-29.75**2 }{ 2 * 25.87 * 29.75 } ) = 26° 33'54" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25.87**2-13.33**2-29.75**2 }{ 2 * 13.33 * 29.75 } ) = 60° 15'18" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29.75**2-13.33**2-25.87**2 }{ 2 * 25.87 * 13.33 } ) = 93° 10'48" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 172.1 }{ 34.47 } = 4.99 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13.33 }{ 2 * sin 26° 33'54" } = 14.9 ; ;




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