Triangle calculator

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

You have entered side a, b and angle α.

Triangle has two solutions: a=13.5; b=16.5; c=3.88988340668 and a=13.5; b=16.5; c=23.14331833947.

#1 Obtuse scalene triangle.

Sides: a = 13.5   b = 16.5   c = 3.88988340668

Area: T = 18.40219845812
Perimeter: p = 33.88988340668
Semiperimeter: s = 16.94444170334

Angle ∠ A = α = 35° = 0.61108652382 rad
Angle ∠ B = β = 135.4989668391° = 135°29'23″ = 2.36547408159 rad
Angle ∠ C = γ = 9.51103316092° = 9°30'37″ = 0.16659865995 rad

Height: ha = 2.7266219938
Height: hb = 2.23105435856
Height: hc = 9.46440111998

Median: ma = 9.90657566697
Median: mb = 5.53438969271
Median: mc = 14.94988876643

Inradius: r = 1.0866020519
Circumradius: R = 11.76882658704

Vertex coordinates: A[3.88988340668; 0] B[0; 0] C[-9.6277174664; 9.46440111998]
Centroid: CG[-1.9132780199; 3.15546703999]
Coordinates of the circumscribed circle: U[1.94444170334; 11.60765207533]
Coordinates of the inscribed circle: I[0.44444170334; 1.0866020519]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145° = 0.61108652382 rad
∠ B' = β' = 44.51103316092° = 44°30'37″ = 2.36547408159 rad
∠ C' = γ' = 170.4989668391° = 170°29'23″ = 0.16659865995 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 = 13.5 ; ; b = 16.5 ; ; c = 3.89 ; ;

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

p = a+b+c = 13.5+16.5+3.89 = 33.89 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 33.89 }{ 2 } = 16.94 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16.94 * (16.94-13.5)(16.94-16.5)(16.94-3.89) } ; ; T = sqrt{ 338.63 } = 18.4 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 18.4 }{ 13.5 } = 2.73 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 18.4 }{ 16.5 } = 2.23 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 18.4 }{ 3.89 } = 9.46 ; ;

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{ 13.5**2-16.5**2-3.89**2 }{ 2 * 16.5 * 3.89 } ) = 35° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16.5**2-13.5**2-3.89**2 }{ 2 * 13.5 * 3.89 } ) = 135° 29'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 3.89**2-13.5**2-16.5**2 }{ 2 * 16.5 * 13.5 } ) = 9° 30'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 18.4 }{ 16.94 } = 1.09 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13.5 }{ 2 * sin 35° } = 11.77 ; ;





#2 Obtuse scalene triangle.

Sides: a = 13.5   b = 16.5   c = 23.14331833947

Area: T = 109.5143673423
Perimeter: p = 53.14331833947
Semiperimeter: s = 26.57215916974

Angle ∠ A = α = 35° = 0.61108652382 rad
Angle ∠ B = β = 44.51103316092° = 44°30'37″ = 0.77768518377 rad
Angle ∠ C = γ = 100.4989668391° = 100°29'23″ = 1.75438755777 rad

Height: ha = 16.22442479146
Height: hb = 13.27443846574
Height: hc = 9.46440111998

Median: ma = 18.93105564847
Median: mb = 17.05547931333
Median: mc = 9.66216906176

Inradius: r = 4.12114570309
Circumradius: R = 11.76882658704

Vertex coordinates: A[23.14331833947; 0] B[0; 0] C[9.6277174664; 9.46440111998]
Centroid: CG[10.92334526862; 3.15546703999]
Coordinates of the circumscribed circle: U[11.57215916974; -2.14325095535]
Coordinates of the inscribed circle: I[10.07215916974; 4.12114570309]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145° = 0.61108652382 rad
∠ B' = β' = 135.4989668391° = 135°29'23″ = 0.77768518377 rad
∠ C' = γ' = 79.51103316092° = 79°30'37″ = 1.75438755777 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 = 13.5 ; ; b = 16.5 ; ; c = 23.14 ; ;

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

p = a+b+c = 13.5+16.5+23.14 = 53.14 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53.14 }{ 2 } = 26.57 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.57 * (26.57-13.5)(26.57-16.5)(26.57-23.14) } ; ; T = sqrt{ 11993.24 } = 109.51 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 109.51 }{ 13.5 } = 16.22 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 109.51 }{ 16.5 } = 13.27 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 109.51 }{ 23.14 } = 9.46 ; ;

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{ 13.5**2-16.5**2-23.14**2 }{ 2 * 16.5 * 23.14 } ) = 35° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16.5**2-13.5**2-23.14**2 }{ 2 * 13.5 * 23.14 } ) = 44° 30'37" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23.14**2-13.5**2-16.5**2 }{ 2 * 16.5 * 13.5 } ) = 100° 29'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 109.51 }{ 26.57 } = 4.12 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13.5 }{ 2 * sin 35° } = 11.77 ; ; : Nr. 1




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