11 24 24 triangle

Acute isosceles triangle.

Sides: a = 11   b = 24   c = 24

Area: T = 128.4877110248
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 26.49660298114° = 26°29'46″ = 0.46224429589 rad
Angle ∠ B = β = 76.75219850943° = 76°45'7″ = 1.34395748473 rad
Angle ∠ C = γ = 76.75219850943° = 76°45'7″ = 1.34395748473 rad

Height: ha = 23.36112927724
Height: hb = 10.70772591874
Height: hc = 10.70772591874

Median: ma = 23.36112927724
Median: mb = 14.33003496461
Median: mc = 14.33003496461

Inradius: r = 4.35554952627
Circumradius: R = 12.32880848712

Vertex coordinates: A[24; 0] B[0; 0] C[2.52108333333; 10.70772591874]
Centroid: CG[8.84402777778; 3.56990863958]
Coordinates of the circumscribed circle: U[12; 2.82551861163]
Coordinates of the inscribed circle: I[5.5; 4.35554952627]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.5043970189° = 153°30'14″ = 0.46224429589 rad
∠ B' = β' = 103.2488014906° = 103°14'53″ = 1.34395748473 rad
∠ C' = γ' = 103.2488014906° = 103°14'53″ = 1.34395748473 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 = 11 ; ; b = 24 ; ; c = 24 ; ;

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

p = a+b+c = 11+24+24 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-11)(29.5-24)(29.5-24) } ; ; T = sqrt{ 16508.94 } = 128.49 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 128.49 }{ 11 } = 23.36 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 128.49 }{ 24 } = 10.71 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 128.49 }{ 24 } = 10.71 ; ;

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{ 11**2-24**2-24**2 }{ 2 * 24 * 24 } ) = 26° 29'46" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-11**2-24**2 }{ 2 * 11 * 24 } ) = 76° 45'7" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-11**2-24**2 }{ 2 * 24 * 11 } ) = 76° 45'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 128.49 }{ 29.5 } = 4.36 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 26° 29'46" } = 12.33 ; ;




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