Triangle calculator

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

You have entered side b, c and angle γ.

Triangle has two solutions: a=12.87702966504; b=49; c=44 and a=36.13297033496; b=49; c=44.

#1 Obtuse scalene triangle.

Sides: a = 12.87702966504   b = 49   c = 44

Area: T = 273.077709441
Perimeter: p = 105.877029665
Semiperimeter: s = 52.93551483252

Angle ∠ A = α = 14.67439575402° = 14°40'26″ = 0.25661088734 rad
Angle ∠ B = β = 105.326604246° = 105°19'34″ = 1.8388286229 rad
Angle ∠ C = γ = 60° = 1.04771975512 rad

Height: ha = 42.43552447854
Height: hb = 11.14660038535
Height: hc = 12.41325952005

Median: ma = 46.12203736545
Median: mb = 21.22766876345
Median: mc = 28.27222879855

Inradius: r = 5.15987102908
Circumradius: R = 25.40334118443

Vertex coordinates: A[44; 0] B[0; 0] C[-3.40217666379; 12.41325952005]
Centroid: CG[13.5332744454; 4.13875317335]
Coordinates of the circumscribed circle: U[22; 12.70217059222]
Coordinates of the inscribed circle: I[3.93551483252; 5.15987102908]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.326604246° = 165°19'34″ = 0.25661088734 rad
∠ B' = β' = 74.67439575402° = 74°40'26″ = 1.8388286229 rad
∠ C' = γ' = 120° = 1.04771975512 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 = 12.87 ; ; b = 49 ; ; c = 44 ; ;

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

p = a+b+c = 12.87+49+44 = 105.87 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 105.87 }{ 2 } = 52.94 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 52.94 * (52.94-12.87)(52.94-49)(52.94-44) } ; ; T = sqrt{ 74571.1 } = 273.08 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 273.08 }{ 12.87 } = 42.44 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 273.08 }{ 49 } = 11.15 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 273.08 }{ 44 } = 12.41 ; ;

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{ 12.87**2-49**2-44**2 }{ 2 * 49 * 44 } ) = 14° 40'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 49**2-12.87**2-44**2 }{ 2 * 12.87 * 44 } ) = 105° 19'34" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 44**2-12.87**2-49**2 }{ 2 * 49 * 12.87 } ) = 60° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 273.08 }{ 52.94 } = 5.16 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12.87 }{ 2 * sin 14° 40'26" } = 25.4 ; ;





#2 Acute scalene triangle.

Sides: a = 36.13297033496   b = 49   c = 44

Area: T = 766.5866402833
Perimeter: p = 129.132970335
Semiperimeter: s = 64.56548516748

Angle ∠ A = α = 45.32660424598° = 45°19'34″ = 0.79110886778 rad
Angle ∠ B = β = 74.67439575402° = 74°40'26″ = 1.30333064246 rad
Angle ∠ C = γ = 60° = 1.04771975512 rad

Height: ha = 42.43552447854
Height: hb = 31.2899240932
Height: hc = 34.84548364924

Median: ma = 42.92204046342
Median: mb = 31.94441345487
Median: mc = 37.00224017067

Inradius: r = 11.87331226503
Circumradius: R = 25.40334118443

Vertex coordinates: A[44; 0] B[0; 0] C[9.54994939106; 34.84548364924]
Centroid: CG[17.85498313035; 11.61549454975]
Coordinates of the circumscribed circle: U[22; 12.70217059222]
Coordinates of the inscribed circle: I[15.56548516748; 11.87331226503]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.674395754° = 134°40'26″ = 0.79110886778 rad
∠ B' = β' = 105.326604246° = 105°19'34″ = 1.30333064246 rad
∠ C' = γ' = 120° = 1.04771975512 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 = 36.13 ; ; b = 49 ; ; c = 44 ; ;

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

p = a+b+c = 36.13+49+44 = 129.13 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 129.13 }{ 2 } = 64.56 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 64.56 * (64.56-36.13)(64.56-49)(64.56-44) } ; ; T = sqrt{ 587654.71 } = 766.59 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 766.59 }{ 36.13 } = 42.44 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 766.59 }{ 49 } = 31.29 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 766.59 }{ 44 } = 34.84 ; ;

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{ 36.13**2-49**2-44**2 }{ 2 * 49 * 44 } ) = 45° 19'34" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 49**2-36.13**2-44**2 }{ 2 * 36.13 * 44 } ) = 74° 40'26" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 44**2-36.13**2-49**2 }{ 2 * 49 * 36.13 } ) = 60° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 766.59 }{ 64.56 } = 11.87 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 36.13 }{ 2 * sin 45° 19'34" } = 25.4 ; ;




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