Triangle calculator

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

You have entered side a, c and angle γ.

Triangle has two solutions: a=380; b=252.6633368508; c=150 and a=380; b=482.4660123602; c=150.

#1 Obtuse scalene triangle.

Sides: a = 380   b = 252.6633368508   c = 150

Area: T = 12181.91440423
Perimeter: p = 782.6633368508
Semiperimeter: s = 391.3321684254

Angle ∠ A = α = 139.9955074621° = 139°59'42″ = 2.44333749887 rad
Angle ∠ B = β = 25.30549253788° = 25°18'18″ = 0.44216542648 rad
Angle ∠ C = γ = 14.7° = 14°42' = 0.25765634 rad

Height: ha = 64.11553370645
Height: hb = 96.42880189422
Height: hc = 162.4265520563

Median: ma = 84.0879658021
Median: mb = 259.7898963495
Median: mc = 313.8388157165

Inradius: r = 31.12993834167
Circumradius: R = 295.5577248947

Vertex coordinates: A[150; 0] B[0; 0] C[343.537740738; 162.4265520563]
Centroid: CG[164.5122469127; 54.14218401878]
Coordinates of the circumscribed circle: U[75; 285.8832996006]
Coordinates of the inscribed circle: I[138.6688315746; 31.12993834167]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 40.00549253788° = 40°18″ = 2.44333749887 rad
∠ B' = β' = 154.6955074621° = 154°41'42″ = 0.44216542648 rad
∠ C' = γ' = 165.3° = 165°18' = 0.25765634 rad




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 = 380 ; ; b = 252.66 ; ; c = 150 ; ;

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

p = a+b+c = 380+252.66+150 = 782.66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 782.66 }{ 2 } = 391.33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 391.33 * (391.33-380)(391.33-252.66)(391.33-150) } ; ; T = sqrt{ 148399029.73 } = 12181.91 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 12181.91 }{ 380 } = 64.12 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 12181.91 }{ 252.66 } = 96.43 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 12181.91 }{ 150 } = 162.43 ; ;

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{ 380**2-252.66**2-150**2 }{ 2 * 252.66 * 150 } ) = 139° 59'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 252.66**2-380**2-150**2 }{ 2 * 380 * 150 } ) = 25° 18'18" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 150**2-380**2-252.66**2 }{ 2 * 252.66 * 380 } ) = 14° 42' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 12181.91 }{ 391.33 } = 31.13 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 380 }{ 2 * sin 139° 59'42" } = 295.56 ; ;





#2 Obtuse scalene triangle.

Sides: a = 380   b = 482.4660123602   c = 150

Area: T = 23261.33769688
Perimeter: p = 1012.46601236
Semiperimeter: s = 506.2330061801

Angle ∠ A = α = 40.00549253788° = 40°18″ = 0.69882176649 rad
Angle ∠ B = β = 125.2955074621° = 125°17'42″ = 2.18768115887 rad
Angle ∠ C = γ = 14.7° = 14°42' = 0.25765634 rad

Height: ha = 122.4288089309
Height: hb = 96.42880189422
Height: hc = 310.1511159583

Median: ma = 302.5465674953
Median: mb = 158.9287836717
Median: mc = 427.7376934848

Inradius: r = 45.95501296427
Circumradius: R = 295.5577248947

Vertex coordinates: A[150; 0] B[0; 0] C[-219.5599236219; 310.1511159583]
Centroid: CG[-23.1866412073; 103.3843719861]
Coordinates of the circumscribed circle: U[75; 285.8832996006]
Coordinates of the inscribed circle: I[23.77699381992; 45.95501296427]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.9955074621° = 139°59'42″ = 0.69882176649 rad
∠ B' = β' = 54.70549253788° = 54°42'18″ = 2.18768115887 rad
∠ C' = γ' = 165.3° = 165°18' = 0.25765634 rad

Calculate another triangle

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 = 380 ; ; b = 482.46 ; ; c = 150 ; ;

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

p = a+b+c = 380+482.46+150 = 1012.46 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1012.46 }{ 2 } = 506.23 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 506.23 * (506.23-380)(506.23-482.46)(506.23-150) } ; ; T = sqrt{ 541089797.57 } = 23261.34 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 23261.34 }{ 380 } = 122.43 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 23261.34 }{ 482.46 } = 96.43 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 23261.34 }{ 150 } = 310.15 ; ;

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{ 380**2-482.46**2-150**2 }{ 2 * 482.46 * 150 } ) = 40° 18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 482.46**2-380**2-150**2 }{ 2 * 380 * 150 } ) = 125° 17'42" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 150**2-380**2-482.46**2 }{ 2 * 482.46 * 380 } ) = 14° 42' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 23261.34 }{ 506.23 } = 45.95 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 380 }{ 2 * sin 40° 18" } = 295.56 ; ;




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