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=39; b=6.24882111848; c=34 and a=39; b=58.41767194745; c=34.

#1 Obtuse scalene triangle.

Sides: a = 39   b = 6.24882111848   c = 34

Area: T = 68.13221294016
Perimeter: p = 79.24882111848
Semiperimeter: s = 39.62441055924

Angle ∠ A = α = 140.102167872° = 140°6'6″ = 2.44552355812 rad
Angle ∠ B = β = 5.89883212804° = 5°53'54″ = 0.10329451267 rad
Angle ∠ C = γ = 34° = 0.59334119457 rad

Height: ha = 3.49439553539
Height: hb = 21.80985232354
Height: hc = 4.00877723177

Median: ma = 14.74400838364
Median: mb = 36.45218856062
Median: mc = 22.15989727087

Inradius: r = 1.71994616354
Circumradius: R = 30.40109580495

Vertex coordinates: A[34; 0] B[0; 0] C[38.79435273087; 4.00877723177]
Centroid: CG[24.26545091029; 1.33659241059]
Coordinates of the circumscribed circle: U[17; 25.20435364647]
Coordinates of the inscribed circle: I[33.37658944076; 1.71994616354]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 39.89883212804° = 39°53'54″ = 2.44552355812 rad
∠ B' = β' = 174.102167872° = 174°6'6″ = 0.10329451267 rad
∠ C' = γ' = 146° = 0.59334119457 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 = 39 ; ; b = 6.25 ; ; c = 34 ; ;

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

p = a+b+c = 39+6.25+34 = 79.25 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 79.25 }{ 2 } = 39.62 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 39.62 * (39.62-39)(39.62-6.25)(39.62-34) } ; ; T = sqrt{ 4641.99 } = 68.13 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 68.13 }{ 39 } = 3.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 68.13 }{ 6.25 } = 21.81 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 68.13 }{ 34 } = 4.01 ; ;

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{ 39**2-6.25**2-34**2 }{ 2 * 6.25 * 34 } ) = 140° 6'6" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 6.25**2-39**2-34**2 }{ 2 * 39 * 34 } ) = 5° 53'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 34**2-39**2-6.25**2 }{ 2 * 6.25 * 39 } ) = 34° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 68.13 }{ 39.62 } = 1.72 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 39 }{ 2 * sin 140° 6'6" } = 30.4 ; ;





#2 Obtuse scalene triangle.

Sides: a = 39   b = 58.41767194745   c = 34

Area: T = 636.9911191996
Perimeter: p = 131.4176719475
Semiperimeter: s = 65.70883597372

Angle ∠ A = α = 39.89883212804° = 39°53'54″ = 0.69663570724 rad
Angle ∠ B = β = 106.102167872° = 106°6'6″ = 1.85218236355 rad
Angle ∠ C = γ = 34° = 0.59334119457 rad

Height: ha = 32.66662149742
Height: hb = 21.80985232354
Height: hc = 37.47700701174

Median: ma = 43.63549235943
Median: mb = 22.03111534301
Median: mc = 46.66664393015

Inradius: r = 9.69442184304
Circumradius: R = 30.40109580495

Vertex coordinates: A[34; 0] B[0; 0] C[-10.81663693259; 37.47700701174]
Centroid: CG[7.72878768914; 12.49900233725]
Coordinates of the circumscribed circle: U[17; 25.20435364647]
Coordinates of the inscribed circle: I[7.29216402628; 9.69442184304]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.102167872° = 140°6'6″ = 0.69663570724 rad
∠ B' = β' = 73.89883212804° = 73°53'54″ = 1.85218236355 rad
∠ C' = γ' = 146° = 0.59334119457 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 = 39 ; ; b = 58.42 ; ; c = 34 ; ;

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

p = a+b+c = 39+58.42+34 = 131.42 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 131.42 }{ 2 } = 65.71 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 65.71 * (65.71-39)(65.71-58.42)(65.71-34) } ; ; T = sqrt{ 405757.78 } = 636.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 636.99 }{ 39 } = 32.67 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 636.99 }{ 58.42 } = 21.81 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 636.99 }{ 34 } = 37.47 ; ;

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{ 39**2-58.42**2-34**2 }{ 2 * 58.42 * 34 } ) = 39° 53'54" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 58.42**2-39**2-34**2 }{ 2 * 39 * 34 } ) = 106° 6'6" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 34**2-39**2-58.42**2 }{ 2 * 58.42 * 39 } ) = 34° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 636.99 }{ 65.71 } = 9.69 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 39 }{ 2 * sin 39° 53'54" } = 30.4 ; ;




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