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=181.4; b=248.6; c=103.5844320765 and a=181.4; b=248.6; c=278.9611138004.

#1 Obtuse scalene triangle.

Sides: a = 181.4   b = 248.6   c = 103.5844320765

Area: T = 8224.475488163
Perimeter: p = 533.5844320765
Semiperimeter: s = 266.7922160383

Angle ∠ A = α = 39.7° = 39°42' = 0.6932895713 rad
Angle ∠ B = β = 118.9087571067° = 118°54'27″ = 2.07553286207 rad
Angle ∠ C = γ = 21.39224289334° = 21°23'33″ = 0.37333683199 rad

Height: ha = 90.67877825979
Height: hb = 66.16663305039
Height: hc = 158.7987679434

Median: ma = 167.4549531962
Median: mb = 79.79656499702
Median: mc = 211.3566410177

Inradius: r = 30.8277273447
Circumradius: R = 141.9922125328

Vertex coordinates: A[103.5844320765; 0] B[0; 0] C[-87.68884086197; 158.7987679434]
Centroid: CG[5.29986373817; 52.93325598115]
Coordinates of the circumscribed circle: U[51.79221603825; 132.2099439065]
Coordinates of the inscribed circle: I[18.19221603825; 30.8277273447]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.3° = 140°18' = 0.6932895713 rad
∠ B' = β' = 61.09224289334° = 61°5'33″ = 2.07553286207 rad
∠ C' = γ' = 158.6087571067° = 158°36'27″ = 0.37333683199 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 = 181.4 ; ; b = 248.6 ; ; c = 103.58 ; ;

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

p = a+b+c = 181.4+248.6+103.58 = 533.58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 533.58 }{ 2 } = 266.79 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 266.79 * (266.79-181.4)(266.79-248.6)(266.79-103.58) } ; ; T = sqrt{ 67641987.08 } = 8224.47 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 8224.47 }{ 181.4 } = 90.68 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 8224.47 }{ 248.6 } = 66.17 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 8224.47 }{ 103.58 } = 158.8 ; ;

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{ 181.4**2-248.6**2-103.58**2 }{ 2 * 248.6 * 103.58 } ) = 39° 42' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 248.6**2-181.4**2-103.58**2 }{ 2 * 181.4 * 103.58 } ) = 118° 54'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 103.58**2-181.4**2-248.6**2 }{ 2 * 248.6 * 181.4 } ) = 21° 23'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 8224.47 }{ 266.79 } = 30.83 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 181.4 }{ 2 * sin 39° 42' } = 141.99 ; ;





#2 Acute scalene triangle.

Sides: a = 181.4   b = 248.6   c = 278.9611138004

Area: T = 22149.19106837
Perimeter: p = 708.9611138004
Semiperimeter: s = 354.4810569002

Angle ∠ A = α = 39.7° = 39°42' = 0.6932895713 rad
Angle ∠ B = β = 61.09224289334° = 61°5'33″ = 1.06662640329 rad
Angle ∠ C = γ = 79.20875710666° = 79°12'27″ = 1.38224329076 rad

Height: ha = 244.2032763878
Height: hb = 178.1911397295
Height: hc = 158.7987679434

Median: ma = 248.1621536622
Median: mb = 199.7880249921
Median: mc = 167.0330329195

Inradius: r = 62.48435114265
Circumradius: R = 141.9922125328

Vertex coordinates: A[278.9611138004; 0] B[0; 0] C[87.68884086197; 158.7987679434]
Centroid: CG[122.2176515541; 52.93325598115]
Coordinates of the circumscribed circle: U[139.4810569002; 26.58882403689]
Coordinates of the inscribed circle: I[105.8810569002; 62.48435114265]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.3° = 140°18' = 0.6932895713 rad
∠ B' = β' = 118.9087571067° = 118°54'27″ = 1.06662640329 rad
∠ C' = γ' = 100.7922428933° = 100°47'33″ = 1.38224329076 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 = 181.4 ; ; b = 248.6 ; ; c = 278.96 ; ;

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

p = a+b+c = 181.4+248.6+278.96 = 708.96 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 708.96 }{ 2 } = 354.48 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 354.48 * (354.48-181.4)(354.48-248.6)(354.48-278.96) } ; ; T = sqrt{ 490586647.94 } = 22149.19 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 22149.19 }{ 181.4 } = 244.2 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 22149.19 }{ 248.6 } = 178.19 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 22149.19 }{ 278.96 } = 158.8 ; ;

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{ 181.4**2-248.6**2-278.96**2 }{ 2 * 248.6 * 278.96 } ) = 39° 42' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 248.6**2-181.4**2-278.96**2 }{ 2 * 181.4 * 278.96 } ) = 61° 5'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 278.96**2-181.4**2-248.6**2 }{ 2 * 248.6 * 181.4 } ) = 79° 12'27" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 22149.19 }{ 354.48 } = 62.48 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 181.4 }{ 2 * sin 39° 42' } = 141.99 ; ; : Nr. 1




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