16 17 24 triangle

Obtuse scalene triangle.

Sides: a = 16   b = 17   c = 24

Area: T = 135.7799002427
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 41.72770936215° = 41°43'38″ = 0.7288275171 rad
Angle ∠ B = β = 45.00661198495° = 45°22″ = 0.78655049749 rad
Angle ∠ C = γ = 93.2676786529° = 93°16' = 1.62878125077 rad

Height: ha = 16.97223753033
Height: hb = 15.97440002855
Height: hc = 11.31549168689

Median: ma = 19.19663538205
Median: mb = 18.54404962177
Median: mc = 11.33657840488

Inradius: r = 4.76441755237
Circumradius: R = 12.02195315243

Vertex coordinates: A[24; 0] B[0; 0] C[11.31325; 11.31549168689]
Centroid: CG[11.77108333333; 3.77216389563]
Coordinates of the circumscribed circle: U[12; -0.68549365391]
Coordinates of the inscribed circle: I[11.5; 4.76441755237]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.2732906379° = 138°16'22″ = 0.7288275171 rad
∠ B' = β' = 134.994388015° = 134°59'38″ = 0.78655049749 rad
∠ C' = γ' = 86.7333213471° = 86°44' = 1.62878125077 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 = 16 ; ; b = 17 ; ; c = 24 ; ;

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

p = a+b+c = 16+17+24 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-16)(28.5-17)(28.5-24) } ; ; T = sqrt{ 18435.94 } = 135.78 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 135.78 }{ 16 } = 16.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 135.78 }{ 17 } = 15.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 135.78 }{ 24 } = 11.31 ; ;

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{ 16**2-17**2-24**2 }{ 2 * 17 * 24 } ) = 41° 43'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-16**2-24**2 }{ 2 * 16 * 24 } ) = 45° 22" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-16**2-17**2 }{ 2 * 17 * 16 } ) = 93° 16' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 135.78 }{ 28.5 } = 4.76 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 41° 43'38" } = 12.02 ; ;




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