9 15 17 triangle

Acute scalene triangle.

Sides: a = 9   b = 15   c = 17

Area: T = 67.36660708369
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 31.89548038856° = 31°53'41″ = 0.55766693421 rad
Angle ∠ B = β = 61.71550959843° = 61°42'54″ = 1.07771316231 rad
Angle ∠ C = γ = 86.39901001302° = 86°23'24″ = 1.50877916884 rad

Height: ha = 14.97702379638
Height: hb = 8.98221427783
Height: hc = 7.92554200985

Median: ma = 15.38766825534
Median: mb = 11.34768057179
Median: mc = 8.98661003778

Inradius: r = 3.28661497969
Circumradius: R = 8.51768986832

Vertex coordinates: A[17; 0] B[0; 0] C[4.26547058824; 7.92554200985]
Centroid: CG[7.08882352941; 2.64218066995]
Coordinates of the circumscribed circle: U[8.5; 0.53662491763]
Coordinates of the inscribed circle: I[5.5; 3.28661497969]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.1055196114° = 148°6'19″ = 0.55766693421 rad
∠ B' = β' = 118.2854904016° = 118°17'6″ = 1.07771316231 rad
∠ C' = γ' = 93.61098998698° = 93°36'36″ = 1.50877916884 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 = 15 ; ; c = 17 ; ;

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

p = a+b+c = 9+15+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 * (20.5-9)(20.5-15)(20.5-17) } ; ; T = sqrt{ 4538.19 } = 67.37 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 67.37 }{ 9 } = 14.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 67.37 }{ 15 } = 8.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 67.37 }{ 17 } = 7.93 ; ;

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**2-15**2-17**2 }{ 2 * 15 * 17 } ) = 31° 53'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-9**2-17**2 }{ 2 * 9 * 17 } ) = 61° 42'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-9**2-15**2 }{ 2 * 15 * 9 } ) = 86° 23'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 67.37 }{ 20.5 } = 3.29 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 31° 53'41" } = 8.52 ; ;




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