17 23 24 triangle

Acute scalene triangle.

Sides: a = 17   b = 23   c = 24

Area: T = 185.9033200618
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 42.34326054522° = 42°20'33″ = 0.7399017879 rad
Angle ∠ B = β = 65.68442608288° = 65°41'3″ = 1.14664066182 rad
Angle ∠ C = γ = 71.9733133719° = 71°58'23″ = 1.25661681564 rad

Height: ha = 21.87109647786
Height: hb = 16.16554957059
Height: hc = 15.49219333848

Median: ma = 21.91546070008
Median: mb = 17.32877234512
Median: mc = 16.27988205961

Inradius: r = 5.80994750193
Circumradius: R = 12.61994707364

Vertex coordinates: A[24; 0] B[0; 0] C[7; 15.49219333848]
Centroid: CG[10.33333333333; 5.16439777949]
Coordinates of the circumscribed circle: U[12; 3.90552582074]
Coordinates of the inscribed circle: I[9; 5.80994750193]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.6577394548° = 137°39'27″ = 0.7399017879 rad
∠ B' = β' = 114.3165739171° = 114°18'57″ = 1.14664066182 rad
∠ C' = γ' = 108.0276866281° = 108°1'37″ = 1.25661681564 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 = 17 ; ; b = 23 ; ; c = 24 ; ;

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

p = a+b+c = 17+23+24 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-17)(32-23)(32-24) } ; ; T = sqrt{ 34560 } = 185.9 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 185.9 }{ 17 } = 21.87 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 185.9 }{ 23 } = 16.17 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 185.9 }{ 24 } = 15.49 ; ;

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{ 17**2-23**2-24**2 }{ 2 * 23 * 24 } ) = 42° 20'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-17**2-24**2 }{ 2 * 17 * 24 } ) = 65° 41'3" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-17**2-23**2 }{ 2 * 23 * 17 } ) = 71° 58'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 185.9 }{ 32 } = 5.81 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 42° 20'33" } = 12.62 ; ;




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