10 15 24 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 15   c = 24

Area: T = 41.07884310801
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 13.19219161626° = 13°11'31″ = 0.23302423717 rad
Angle ∠ B = β = 20.01882999855° = 20°1'6″ = 0.34993852454 rad
Angle ∠ C = γ = 146.7989783852° = 146°47'23″ = 2.56219650365 rad

Height: ha = 8.2165686216
Height: hb = 5.4777124144
Height: hc = 3.423320259

Median: ma = 19.37878223751
Median: mb = 16.78554103316
Median: mc = 4.30111626335

Inradius: r = 1.67766706563
Circumradius: R = 21.90993080319

Vertex coordinates: A[24; 0] B[0; 0] C[9.39658333333; 3.423320259]
Centroid: CG[11.13219444444; 1.141106753]
Coordinates of the circumscribed circle: U[12; -18.331078772]
Coordinates of the inscribed circle: I[9.5; 1.67766706563]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.8088083837° = 166°48'29″ = 0.23302423717 rad
∠ B' = β' = 159.9821700014° = 159°58'54″ = 0.34993852454 rad
∠ C' = γ' = 33.21102161481° = 33°12'37″ = 2.56219650365 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 = 10 ; ; b = 15 ; ; c = 24 ; ;

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

p = a+b+c = 10+15+24 = 49 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 49 }{ 2 } = 24.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24.5 * (24.5-10)(24.5-15)(24.5-24) } ; ; T = sqrt{ 1687.44 } = 41.08 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 41.08 }{ 10 } = 8.22 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 41.08 }{ 15 } = 5.48 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 41.08 }{ 24 } = 3.42 ; ;

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{ 10**2-15**2-24**2 }{ 2 * 15 * 24 } ) = 13° 11'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-10**2-24**2 }{ 2 * 10 * 24 } ) = 20° 1'6" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-10**2-15**2 }{ 2 * 15 * 10 } ) = 146° 47'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 41.08 }{ 24.5 } = 1.68 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 13° 11'31" } = 21.91 ; ;




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