15 16 28 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 16   c = 28

Area: T = 93.07695304598
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 24.55501133573° = 24°33' = 0.42884803098 rad
Angle ∠ B = β = 26.30774810463° = 26°18'27″ = 0.45991521622 rad
Angle ∠ C = γ = 129.1422405596° = 129°8'33″ = 2.25439601816 rad

Height: ha = 12.4099270728
Height: hb = 11.63436913075
Height: hc = 6.64878236043

Median: ma = 21.53548554674
Median: mb = 20.98880918618
Median: mc = 6.67108320321

Inradius: r = 3.15548993376
Circumradius: R = 18.05110204758

Vertex coordinates: A[28; 0] B[0; 0] C[13.44664285714; 6.64878236043]
Centroid: CG[13.81554761905; 2.21659412014]
Coordinates of the circumscribed circle: U[14; -11.39547066753]
Coordinates of the inscribed circle: I[13.5; 3.15548993376]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.4549886643° = 155°27' = 0.42884803098 rad
∠ B' = β' = 153.6932518954° = 153°41'33″ = 0.45991521622 rad
∠ C' = γ' = 50.85875944036° = 50°51'27″ = 2.25439601816 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 = 16 ; ; c = 28 ; ;

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

p = a+b+c = 15+16+28 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-15)(29.5-16)(29.5-28) } ; ; T = sqrt{ 8661.94 } = 93.07 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 93.07 }{ 15 } = 12.41 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 93.07 }{ 16 } = 11.63 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 93.07 }{ 28 } = 6.65 ; ;

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**2-16**2-28**2 }{ 2 * 16 * 28 } ) = 24° 33' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-15**2-28**2 }{ 2 * 15 * 28 } ) = 26° 18'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-15**2-16**2 }{ 2 * 16 * 15 } ) = 129° 8'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 93.07 }{ 29.5 } = 3.15 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 24° 33' } = 18.05 ; ;




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