Triangle calculator ASA

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


Obtuse scalene triangle.

Sides: a = 72.1655379808   b = 131.2121805798   c = 100

Area: T = 3573.154356462
Perimeter: p = 303.3777185606
Semiperimeter: s = 151.6898592803

Angle ∠ A = α = 33° = 0.57659586532 rad
Angle ∠ B = β = 98° = 1.7110422667 rad
Angle ∠ C = γ = 49° = 0.85552113335 rad

Height: ha = 99.02768068742
Height: hb = 54.46439035015
Height: hc = 71.46330712925

Median: ma = 110.9343802241
Median: mb = 57.44437683845
Median: mc = 93.33991129796

Inradius: r = 23.55658488519
Circumradius: R = 66.25106496674

Vertex coordinates: A[100; 0] B[0; 0] C[-10.04334796898; 71.46330712925]
Centroid: CG[29.98655067701; 23.82110237642]
Coordinates of the circumscribed circle: U[50; 43.46443368908]
Coordinates of the inscribed circle: I[20.47767870049; 23.55658488519]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147° = 0.57659586532 rad
∠ B' = β' = 82° = 1.7110422667 rad
∠ C' = γ' = 131° = 0.85552113335 rad

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How did we calculate this triangle?

1. Calculate the third unknown inner angle

 alpha = 33° ; ; beta = 98° ; ; ; ; alpha + beta + gamma = 180° ; ; ; ; gamma = 180° - alpha - beta = 180° - 33° - 98° = 49° ; ;

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

c = 100 ; ; ; ; fraction{ a }{ c } = fraction{ sin alpha }{ sin gamma } ; ; ; ; a = c * fraction{ sin alpha }{ sin gamma } ; ; ; ; a = 100 * fraction{ sin 33° }{ sin 49° } = 72.17 ; ;

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 = 100 * fraction{ sin 98° }{ sin 49° } = 131.21 ; ;
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 = 72.17 ; ; b = 131.21 ; ; c = 100 ; ;

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

p = a+b+c = 72.17+131.21+100 = 303.38 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 303.38 }{ 2 } = 151.69 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 151.69 * (151.69-72.17)(151.69-131.21)(151.69-100) } ; ; T = sqrt{ 12767426.4 } = 3573.15 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3573.15 }{ 72.17 } = 99.03 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3573.15 }{ 131.21 } = 54.46 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3573.15 }{ 100 } = 71.46 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 131.21**2+100**2-72.17**2 }{ 2 * 131.21 * 100 } ) = 33° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 72.17**2+100**2-131.21**2 }{ 2 * 72.17 * 100 } ) = 98° ; ;
 gamma = 180° - alpha - beta = 180° - 33° - 98° = 49° ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3573.15 }{ 151.69 } = 23.56 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 72.17 }{ 2 * sin 33° } = 66.25 ; ;

11. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 131.21**2+2 * 100**2 - 72.17**2 } }{ 2 } = 110.934 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 100**2+2 * 72.17**2 - 131.21**2 } }{ 2 } = 57.444 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 131.21**2+2 * 72.17**2 - 100**2 } }{ 2 } = 93.339 ; ;
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