13 17 18 triangle

Acute scalene triangle.

Sides: a = 13   b = 17   c = 18

Area: T = 105.3299572649
Perimeter: p = 48
Semiperimeter: s = 24

Angle ∠ A = α = 43.4990358347° = 43°29'25″ = 0.7599049946 rad
Angle ∠ B = β = 64.15875871263° = 64°9'27″ = 1.12197611355 rad
Angle ∠ C = γ = 72.35220545267° = 72°21'7″ = 1.26327815721 rad

Height: ha = 16.21999342536
Height: hb = 12.38881850175
Height: hc = 11.76999525165

Median: ma = 16.2565768207
Median: mb = 13.22003787824
Median: mc = 12.16655250606

Inradius: r = 4.38774821937
Circumradius: R = 9.44444827741

Vertex coordinates: A[18; 0] B[0; 0] C[5.66766666667; 11.76999525165]
Centroid: CG[7.88988888889; 3.98999841722]
Coordinates of the circumscribed circle: U[9; 2.86332594835]
Coordinates of the inscribed circle: I[7; 4.38774821937]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 136.5109641653° = 136°30'35″ = 0.7599049946 rad
∠ B' = β' = 115.8422412874° = 115°50'33″ = 1.12197611355 rad
∠ C' = γ' = 107.6487945473° = 107°38'53″ = 1.26327815721 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 = 13 ; ; b = 17 ; ; c = 18 ; ;

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

p = a+b+c = 13+17+18 = 48 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 48 }{ 2 } = 24 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24 * (24-13)(24-17)(24-18) } ; ; T = sqrt{ 11088 } = 105.3 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 105.3 }{ 13 } = 16.2 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 105.3 }{ 17 } = 12.39 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 105.3 }{ 18 } = 11.7 ; ;

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**2-17**2-18**2 }{ 2 * 17 * 18 } ) = 43° 29'25" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-13**2-18**2 }{ 2 * 13 * 18 } ) = 64° 9'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-13**2-17**2 }{ 2 * 17 * 13 } ) = 72° 21'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 105.3 }{ 24 } = 4.39 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 43° 29'25" } = 9.44 ; ;




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