15 17 24 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 17   c = 24

Area: T = 126.5544336156
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 38.34327492605° = 38°20'34″ = 0.66992072189 rad
Angle ∠ B = β = 44.67546095644° = 44°40'29″ = 0.78797190289 rad
Angle ∠ C = γ = 96.98326411751° = 96°58'58″ = 1.69326664058 rad

Height: ha = 16.87439114875
Height: hb = 14.88987454302
Height: hc = 10.54661946797

Median: ma = 19.39771647413
Median: mb = 18.1187670932
Median: mc = 10.63301458127

Inradius: r = 4.52197977199
Circumradius: R = 12.09896687262

Vertex coordinates: A[24; 0] B[0; 0] C[10.66766666667; 10.54661946797]
Centroid: CG[11.55655555556; 3.51553982266]
Coordinates of the circumscribed circle: U[12; -1.47697244334]
Coordinates of the inscribed circle: I[11; 4.52197977199]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.657725074° = 141°39'26″ = 0.66992072189 rad
∠ B' = β' = 135.3255390436° = 135°19'31″ = 0.78797190289 rad
∠ C' = γ' = 83.01773588249° = 83°1'2″ = 1.69326664058 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 = 24 ; ;

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

p = a+b+c = 15+17+24 = 56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 56 }{ 2 } = 28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28 * (28-15)(28-17)(28-24) } ; ; T = sqrt{ 16016 } = 126.55 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 126.55 }{ 15 } = 16.87 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 126.55 }{ 17 } = 14.89 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 126.55 }{ 24 } = 10.55 ; ;

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**2-24**2 }{ 2 * 17 * 24 } ) = 38° 20'34" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-15**2-24**2 }{ 2 * 15 * 24 } ) = 44° 40'29" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-15**2-17**2 }{ 2 * 17 * 15 } ) = 96° 58'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 126.55 }{ 28 } = 4.52 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 38° 20'34" } = 12.09 ; ;




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