17 18 27 triangle

Obtuse scalene triangle.

Sides: a = 17   b = 18   c = 27

Area: T = 150.2266495666
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 38.18659763611° = 38°11'10″ = 0.66664710156 rad
Angle ∠ B = β = 40.88879383595° = 40°53'17″ = 0.71436291487 rad
Angle ∠ C = γ = 100.9266085279° = 100°55'34″ = 1.76114924893 rad

Height: ha = 17.67437053724
Height: hb = 16.69218328517
Height: hc = 11.12878885678

Median: ma = 21.31331414859
Median: mb = 20.68881608656
Median: mc = 11.14767484048

Inradius: r = 4.84660159892
Circumradius: R = 13.74992390463

Vertex coordinates: A[27; 0] B[0; 0] C[12.85218518519; 11.12878885678]
Centroid: CG[13.28439506173; 3.70992961893]
Coordinates of the circumscribed circle: U[13.5; -2.60660649173]
Coordinates of the inscribed circle: I[13; 4.84660159892]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.8144023639° = 141°48'50″ = 0.66664710156 rad
∠ B' = β' = 139.112206164° = 139°6'43″ = 0.71436291487 rad
∠ C' = γ' = 79.07439147206° = 79°4'26″ = 1.76114924893 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 = 17 ; ; b = 18 ; ; c = 27 ; ;

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

p = a+b+c = 17+18+27 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-17)(31-18)(31-27) } ; ; T = sqrt{ 22568 } = 150.23 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 150.23 }{ 17 } = 17.67 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 150.23 }{ 18 } = 16.69 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 150.23 }{ 27 } = 11.13 ; ;

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{ 17**2-18**2-27**2 }{ 2 * 18 * 27 } ) = 38° 11'10" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-17**2-27**2 }{ 2 * 17 * 27 } ) = 40° 53'17" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-17**2-18**2 }{ 2 * 18 * 17 } ) = 100° 55'34" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 150.23 }{ 31 } = 4.85 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 38° 11'10" } = 13.75 ; ;




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