8 16 17 triangle

Acute scalene triangle.

Sides: a = 8   b = 16   c = 17

Area: T = 63.52990287979
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 27.84878490371° = 27°50'52″ = 0.48660366553 rad
Angle ∠ B = β = 69.10773811539° = 69°6'27″ = 1.20661513386 rad
Angle ∠ C = γ = 83.0454769809° = 83°2'41″ = 1.44994046597 rad

Height: ha = 15.88222571995
Height: hb = 7.94111285997
Height: hc = 7.4744003388

Median: ma = 16.0165617378
Median: mb = 10.60766017178
Median: mc = 9.36774969976

Inradius: r = 3.09989770145
Circumradius: R = 8.56330145824

Vertex coordinates: A[17; 0] B[0; 0] C[2.85329411765; 7.4744003388]
Centroid: CG[6.61876470588; 2.49113344627]
Coordinates of the circumscribed circle: U[8.5; 1.03769275471]
Coordinates of the inscribed circle: I[4.5; 3.09989770145]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.1522150963° = 152°9'8″ = 0.48660366553 rad
∠ B' = β' = 110.8932618846° = 110°53'33″ = 1.20661513386 rad
∠ C' = γ' = 96.9555230191° = 96°57'19″ = 1.44994046597 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 = 8 ; ; b = 16 ; ; c = 17 ; ;

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

p = a+b+c = 8+16+17 = 41 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 41 }{ 2 } = 20.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.5 * (20.5-8)(20.5-16)(20.5-17) } ; ; T = sqrt{ 4035.94 } = 63.53 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 63.53 }{ 8 } = 15.88 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 63.53 }{ 16 } = 7.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 63.53 }{ 17 } = 7.47 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 16**2+17**2-8**2 }{ 2 * 16 * 17 } ) = 27° 50'52" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 8**2+17**2-16**2 }{ 2 * 8 * 17 } ) = 69° 6'27" ; ; gamma = 180° - alpha - beta = 180° - 27° 50'52" - 69° 6'27" = 83° 2'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 63.53 }{ 20.5 } = 3.1 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 8 }{ 2 * sin 27° 50'52" } = 8.56 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 17**2 - 8**2 } }{ 2 } = 16.016 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 17**2+2 * 8**2 - 16**2 } }{ 2 } = 10.607 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 8**2 - 17**2 } }{ 2 } = 9.367 ; ;
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