9 16 17 triangle

Acute scalene triangle.

Sides: a = 9   b = 16   c = 17

Area: T = 70.99329573972
Perimeter: p = 42
Semiperimeter: s = 21

Angle ∠ A = α = 31.46769762933° = 31°28'1″ = 0.5499202342 rad
Angle ∠ B = β = 68.12770919336° = 68°7'38″ = 1.18990420641 rad
Angle ∠ C = γ = 80.40659317731° = 80°24'21″ = 1.40333482476 rad

Height: ha = 15.77662127549
Height: hb = 8.87441196746
Height: hc = 8.3522112635

Median: ma = 15.88223801743
Median: mb = 11
Median: mc = 9.81107084352

Inradius: r = 3.38106170189
Circumradius: R = 8.62105733982

Vertex coordinates: A[17; 0] B[0; 0] C[3.35329411765; 8.3522112635]
Centroid: CG[6.78443137255; 2.7844037545]
Coordinates of the circumscribed circle: U[8.5; 1.4376762233]
Coordinates of the inscribed circle: I[5; 3.38106170189]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.5333023707° = 148°31'59″ = 0.5499202342 rad
∠ B' = β' = 111.8732908066° = 111°52'22″ = 1.18990420641 rad
∠ C' = γ' = 99.59440682269° = 99°35'39″ = 1.40333482476 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 = 9 ; ; b = 16 ; ; c = 17 ; ;

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

p = a+b+c = 9+16+17 = 42 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 42 }{ 2 } = 21 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21 * (21-9)(21-16)(21-17) } ; ; T = sqrt{ 5040 } = 70.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 70.99 }{ 9 } = 15.78 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 70.99 }{ 16 } = 8.87 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 70.99 }{ 17 } = 8.35 ; ;

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{ 9**2-16**2-17**2 }{ 2 * 16 * 17 } ) = 31° 28'1" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-9**2-17**2 }{ 2 * 9 * 17 } ) = 68° 7'38" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-9**2-16**2 }{ 2 * 16 * 9 } ) = 80° 24'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 70.99 }{ 21 } = 3.38 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 31° 28'1" } = 8.62 ; ;




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