17 24 24 triangle

Acute isosceles triangle.

Sides: a = 17   b = 24   c = 24

Area: T = 190.7777193343
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 41.4854759909° = 41°29'5″ = 0.72440456498 rad
Angle ∠ B = β = 69.25876200455° = 69°15'27″ = 1.20987735019 rad
Angle ∠ C = γ = 69.25876200455° = 69°15'27″ = 1.20987735019 rad

Height: ha = 22.44443756875
Height: hb = 15.89880994453
Height: hc = 15.89880994453

Median: ma = 22.44443756875
Median: mb = 16.98552877515
Median: mc = 16.98552877515

Inradius: r = 5.87700674875
Circumradius: R = 12.83217224774

Vertex coordinates: A[24; 0] B[0; 0] C[6.02108333333; 15.89880994453]
Centroid: CG[10.00769444444; 5.29993664818]
Coordinates of the circumscribed circle: U[12; 4.54545683774]
Coordinates of the inscribed circle: I[8.5; 5.87700674875]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.5155240091° = 138°30'55″ = 0.72440456498 rad
∠ B' = β' = 110.7422379954° = 110°44'33″ = 1.20987735019 rad
∠ C' = γ' = 110.7422379954° = 110°44'33″ = 1.20987735019 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 = 24 ; ; c = 24 ; ;

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

p = a+b+c = 17+24+24 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-17)(32.5-24)(32.5-24) } ; ; T = sqrt{ 36395.94 } = 190.78 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 190.78 }{ 17 } = 22.44 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 190.78 }{ 24 } = 15.9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 190.78 }{ 24 } = 15.9 ; ;

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**2-24**2-24**2 }{ 2 * 24 * 24 } ) = 41° 29'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-17**2-24**2 }{ 2 * 17 * 24 } ) = 69° 15'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-17**2-24**2 }{ 2 * 24 * 17 } ) = 69° 15'27" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 190.78 }{ 32.5 } = 5.87 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 41° 29'5" } = 12.83 ; ;




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