Triangle calculator

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side a, angle α and angle β.

Acute scalene triangle.

Sides: a = 42   b = 30.0366200402   c = 34.19899583527

Area: T = 507.6954979393
Perimeter: p = 106.2266158755
Semiperimeter: s = 53.11330793773

Angle ∠ A = α = 81.4° = 81°24' = 1.42106980111 rad
Angle ∠ B = β = 45° = 0.78553981634 rad
Angle ∠ C = γ = 53.6° = 53°36' = 0.93554964791 rad

Height: ha = 24.17659513997
Height: hb = 33.80655394889
Height: hc = 29.69884848098

Median: ma = 24.3843668579
Median: mb = 35.22768830928
Median: mc = 32.26221814863

Inradius: r = 9.55987562488
Circumradius: R = 21.23988009853

Vertex coordinates: A[34.19899583527; 0] B[0; 0] C[29.69884848098; 29.69884848098]
Centroid: CG[21.29661477208; 9.89994949366]
Coordinates of the circumscribed circle: U[17.09549791763; 12.60435056335]
Coordinates of the inscribed circle: I[23.07768789754; 9.55987562488]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 98.6° = 98°36' = 1.42106980111 rad
∠ B' = β' = 135° = 0.78553981634 rad
∠ C' = γ' = 126.4° = 126°24' = 0.93554964791 rad

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How did we calculate this triangle?

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 = 42 ; ; b = 30.04 ; ; c = 34.19 ; ;

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

p = a+b+c = 42+30.04+34.19 = 106.23 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 106.23 }{ 2 } = 53.11 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 53.11 * (53.11-42)(53.11-30.04)(53.11-34.19) } ; ; T = sqrt{ 257754.19 } = 507.69 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 507.69 }{ 42 } = 24.18 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 507.69 }{ 30.04 } = 33.81 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 507.69 }{ 34.19 } = 29.7 ; ;

5. 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{ 42**2-30.04**2-34.19**2 }{ 2 * 30.04 * 34.19 } ) = 81° 24' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 30.04**2-42**2-34.19**2 }{ 2 * 42 * 34.19 } ) = 45° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 34.19**2-42**2-30.04**2 }{ 2 * 30.04 * 42 } ) = 53° 36' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 507.69 }{ 53.11 } = 9.56 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 42 }{ 2 * sin 81° 24' } = 21.24 ; ;




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