3 17 18 triangle

Obtuse scalene triangle.

Sides: a = 3   b = 17   c = 18

Area: T = 24.65876560119
Perimeter: p = 38
Semiperimeter: s = 19

Angle ∠ A = α = 9.27442999592° = 9°16'27″ = 0.16218670701 rad
Angle ∠ B = β = 65.95879240942° = 65°57'29″ = 1.15111829432 rad
Angle ∠ C = γ = 104.7687775947° = 104°46'4″ = 1.82985426403 rad

Height: ha = 16.43884373413
Height: hb = 2.90109007073
Height: hc = 2.74397395569

Median: ma = 17.44327635425
Median: mb = 9.70882439195
Median: mc = 8.24662112512

Inradius: r = 1.2987771369
Circumradius: R = 9.30774540374

Vertex coordinates: A[18; 0] B[0; 0] C[1.22222222222; 2.74397395569]
Centroid: CG[6.40774074074; 0.9133246519]
Coordinates of the circumscribed circle: U[9; -2.3722488284]
Coordinates of the inscribed circle: I[2; 1.2987771369]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.7265700041° = 170°43'33″ = 0.16218670701 rad
∠ B' = β' = 114.0422075906° = 114°2'31″ = 1.15111829432 rad
∠ C' = γ' = 75.23222240535° = 75°13'56″ = 1.82985426403 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 = 3 ; ; b = 17 ; ; c = 18 ; ;

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

p = a+b+c = 3+17+18 = 38 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 38 }{ 2 } = 19 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19 * (19-3)(19-17)(19-18) } ; ; T = sqrt{ 608 } = 24.66 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 24.66 }{ 3 } = 16.44 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 24.66 }{ 17 } = 2.9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 24.66 }{ 18 } = 2.74 ; ;

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{ 3**2-17**2-18**2 }{ 2 * 17 * 18 } ) = 9° 16'27" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-3**2-18**2 }{ 2 * 3 * 18 } ) = 65° 57'29" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-3**2-17**2 }{ 2 * 17 * 3 } ) = 104° 46'4" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 24.66 }{ 19 } = 1.3 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 9° 16'27" } = 9.31 ; ;




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