3 16 17 triangle

Obtuse scalene triangle.

Sides: a = 3   b = 16   c = 17

Area: T = 23.23879000772
Perimeter: p = 36
Semiperimeter: s = 18

Angle ∠ A = α = 9.83882269853° = 9°50'18″ = 0.17217094535 rad
Angle ∠ B = β = 65.68442608288° = 65°41'3″ = 1.14664066182 rad
Angle ∠ C = γ = 104.4787512186° = 104°28'39″ = 1.82334765819 rad

Height: ha = 15.49219333848
Height: hb = 2.90547375097
Height: hc = 2.73438705973

Median: ma = 16.43992822228
Median: mb = 9.22195444573
Median: mc = 7.76220873481

Inradius: r = 1.29109944487
Circumradius: R = 8.77987622514

Vertex coordinates: A[17; 0] B[0; 0] C[1.23552941176; 2.73438705973]
Centroid: CG[6.07884313725; 0.91112901991]
Coordinates of the circumscribed circle: U[8.5; -2.19546905629]
Coordinates of the inscribed circle: I[2; 1.29109944487]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.1621773015° = 170°9'42″ = 0.17217094535 rad
∠ B' = β' = 114.3165739171° = 114°18'57″ = 1.14664066182 rad
∠ C' = γ' = 75.52224878141° = 75°31'21″ = 1.82334765819 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 = 16 ; ; c = 17 ; ;

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

p = a+b+c = 3+16+17 = 36 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 36 }{ 2 } = 18 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18 * (18-3)(18-16)(18-17) } ; ; T = sqrt{ 540 } = 23.24 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 23.24 }{ 3 } = 15.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 23.24 }{ 16 } = 2.9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 23.24 }{ 17 } = 2.73 ; ;

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**2-16**2-17**2 }{ 2 * 16 * 17 } ) = 9° 50'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-3**2-17**2 }{ 2 * 3 * 17 } ) = 65° 41'3" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-3**2-16**2 }{ 2 * 16 * 3 } ) = 104° 28'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 23.24 }{ 18 } = 1.29 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 9° 50'18" } = 8.78 ; ;




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