10 16 17 triangle

Acute scalene triangle.

Sides: a = 10   b = 16   c = 17

Area: T = 78.22768336314
Perimeter: p = 43
Semiperimeter: s = 21.5

Angle ∠ A = α = 35.11334508335° = 35°6'48″ = 0.61328453288 rad
Angle ∠ B = β = 66.97222773387° = 66°58'20″ = 1.16988867471 rad
Angle ∠ C = γ = 77.91442718278° = 77°54'51″ = 1.36598605777 rad

Height: ha = 15.64553667263
Height: hb = 9.77883542039
Height: hc = 9.20331568978

Median: ma = 15.73221327226
Median: mb = 11.42436596588
Median: mc = 10.28334819006

Inradius: r = 3.63884573782
Circumradius: R = 8.69326693621

Vertex coordinates: A[17; 0] B[0; 0] C[3.91217647059; 9.20331568978]
Centroid: CG[6.97105882353; 3.06877189659]
Coordinates of the circumscribed circle: U[8.5; 1.82200276477]
Coordinates of the inscribed circle: I[5.5; 3.63884573782]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.8876549167° = 144°53'12″ = 0.61328453288 rad
∠ B' = β' = 113.0287722661° = 113°1'40″ = 1.16988867471 rad
∠ C' = γ' = 102.0865728172° = 102°5'9″ = 1.36598605777 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 = 10 ; ; b = 16 ; ; c = 17 ; ;

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

p = a+b+c = 10+16+17 = 43 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 43 }{ 2 } = 21.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21.5 * (21.5-10)(21.5-16)(21.5-17) } ; ; T = sqrt{ 6119.44 } = 78.23 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 78.23 }{ 10 } = 15.65 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 78.23 }{ 16 } = 9.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 78.23 }{ 17 } = 9.2 ; ;

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**2-10**2 }{ 2 * 16 * 17 } ) = 35° 6'48" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 10**2+17**2-16**2 }{ 2 * 10 * 17 } ) = 66° 58'20" ; ; gamma = 180° - alpha - beta = 180° - 35° 6'48" - 66° 58'20" = 77° 54'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 78.23 }{ 21.5 } = 3.64 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 10 }{ 2 * sin 35° 6'48" } = 8.69 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 17**2 - 10**2 } }{ 2 } = 15.732 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 17**2+2 * 10**2 - 16**2 } }{ 2 } = 11.424 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 10**2 - 17**2 } }{ 2 } = 10.283 ; ;
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