15 17 28 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 17   c = 28

Area: T = 108.1676538264
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 27.03215621153° = 27°1'54″ = 0.47217897609 rad
Angle ∠ B = β = 31.00327191339° = 31°10″ = 0.5411099526 rad
Angle ∠ C = γ = 121.9665718751° = 121°57'57″ = 2.12987033668 rad

Height: ha = 14.42222051019
Height: hb = 12.72554750899
Height: hc = 7.72661813046

Median: ma = 21.91546070008
Median: mb = 20.79106228863
Median: mc = 7.81102496759

Inradius: r = 3.60655512755
Circumradius: R = 16.50223308377

Vertex coordinates: A[28; 0] B[0; 0] C[12.85771428571; 7.72661813046]
Centroid: CG[13.6199047619; 2.57553937682]
Coordinates of the circumscribed circle: U[14; -8.73765280905]
Coordinates of the inscribed circle: I[13; 3.60655512755]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.9688437885° = 152°58'6″ = 0.47217897609 rad
∠ B' = β' = 148.9977280866° = 148°59'50″ = 0.5411099526 rad
∠ C' = γ' = 58.03442812492° = 58°2'3″ = 2.12987033668 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 = 15 ; ; b = 17 ; ; c = 28 ; ;

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

p = a+b+c = 15+17+28 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-15)(30-17)(30-28) } ; ; T = sqrt{ 11700 } = 108.17 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 108.17 }{ 15 } = 14.42 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 108.17 }{ 17 } = 12.73 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 108.17 }{ 28 } = 7.73 ; ;

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{ 15**2-17**2-28**2 }{ 2 * 17 * 28 } ) = 27° 1'54" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-15**2-28**2 }{ 2 * 15 * 28 } ) = 31° 10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-15**2-17**2 }{ 2 * 17 * 15 } ) = 121° 57'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 108.17 }{ 30 } = 3.61 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 27° 1'54" } = 16.5 ; ;




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