15 16 24 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 16   c = 24

Area: T = 117.6266261949
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 37.78804045667° = 37°46'49″ = 0.65993924524 rad
Angle ∠ B = β = 40.80444376906° = 40°48'16″ = 0.71221717871 rad
Angle ∠ C = γ = 101.4155157743° = 101°24'55″ = 1.7770028414 rad

Height: ha = 15.68435015931
Height: hb = 14.70332827436
Height: hc = 9.80221884957

Median: ma = 18.96770767384
Median: mb = 18.34439363278
Median: mc = 9.82334413522

Inradius: r = 4.27773186163
Circumradius: R = 12.24221640894

Vertex coordinates: A[24; 0] B[0; 0] C[11.35441666667; 9.80221884957]
Centroid: CG[11.78547222222; 3.26773961652]
Coordinates of the circumscribed circle: U[12; -2.42329283094]
Coordinates of the inscribed circle: I[11.5; 4.27773186163]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.2219595433° = 142°13'11″ = 0.65993924524 rad
∠ B' = β' = 139.1965562309° = 139°11'44″ = 0.71221717871 rad
∠ C' = γ' = 78.58548422573° = 78°35'5″ = 1.7770028414 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 = 24 ; ;

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

p = a+b+c = 15+16+24 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-15)(27.5-16)(27.5-24) } ; ; T = sqrt{ 13835.94 } = 117.63 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 117.63 }{ 15 } = 15.68 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 117.63 }{ 16 } = 14.7 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 117.63 }{ 24 } = 9.8 ; ;

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**2-24**2 }{ 2 * 16 * 24 } ) = 37° 46'49" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-15**2-24**2 }{ 2 * 15 * 24 } ) = 40° 48'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-15**2-16**2 }{ 2 * 16 * 15 } ) = 101° 24'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 117.63 }{ 27.5 } = 4.28 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 37° 46'49" } = 12.24 ; ;




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