Triangle calculator

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

You have entered side a, b and c.

Obtuse scalene triangle.

Sides: a = 40   b = 55   c = 85

Area: T = 887.4121967465
Perimeter: p = 180
Semiperimeter: s = 90

Angle ∠ A = α = 22.31114770869° = 22°18'41″ = 0.38994087361 rad
Angle ∠ B = β = 31.46769762933° = 31°28'1″ = 0.5499202342 rad
Angle ∠ C = γ = 126.222154662° = 126°13'18″ = 2.20329815755 rad

Height: ha = 44.37105983732
Height: hb = 32.27695260896
Height: hc = 20.88802815874

Median: ma = 68.73986354243
Median: mb = 60.46769331122
Median: mc = 22.5

Inradius: r = 9.86601329718
Circumradius: R = 52.68112818781

Vertex coordinates: A[85; 0] B[0; 0] C[34.11876470588; 20.88802815874]
Centroid: CG[39.70658823529; 6.96600938625]
Coordinates of the circumscribed circle: U[42.5; -31.13298483825]
Coordinates of the inscribed circle: I[35; 9.86601329718]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.6898522913° = 157°41'19″ = 0.38994087361 rad
∠ B' = β' = 148.5333023707° = 148°31'59″ = 0.5499202342 rad
∠ C' = γ' = 53.77884533802° = 53°46'42″ = 2.20329815755 rad

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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 = 40 ; ; b = 55 ; ; c = 85 ; ;

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

p = a+b+c = 40+55+85 = 180 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 180 }{ 2 } = 90 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 90 * (90-40)(90-55)(90-85) } ; ; T = sqrt{ 787500 } = 887.41 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 887.41 }{ 40 } = 44.37 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 887.41 }{ 55 } = 32.27 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 887.41 }{ 85 } = 20.88 ; ;

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{ 40**2-55**2-85**2 }{ 2 * 55 * 85 } ) = 22° 18'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 55**2-40**2-85**2 }{ 2 * 40 * 85 } ) = 31° 28'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 85**2-40**2-55**2 }{ 2 * 55 * 40 } ) = 126° 13'18" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 887.41 }{ 90 } = 9.86 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 40 }{ 2 * sin 22° 18'41" } = 52.68 ; ;




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