5 24 24 triangle

Acute isosceles triangle.

Sides: a = 5   b = 24   c = 24

Area: T = 59.67435913114
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 11.95883135926° = 11°57'30″ = 0.20987119452 rad
Angle ∠ B = β = 84.02108432037° = 84°1'15″ = 1.46664403542 rad
Angle ∠ C = γ = 84.02108432037° = 84°1'15″ = 1.46664403542 rad

Height: ha = 23.86994365246
Height: hb = 4.9732799276
Height: hc = 4.9732799276

Median: ma = 23.86994365246
Median: mb = 12.51099960032
Median: mc = 12.51099960032

Inradius: r = 2.25218336344
Circumradius: R = 12.06656388224

Vertex coordinates: A[24; 0] B[0; 0] C[0.52108333333; 4.9732799276]
Centroid: CG[8.17436111111; 1.65875997587]
Coordinates of the circumscribed circle: U[12; 1.25768373773]
Coordinates of the inscribed circle: I[2.5; 2.25218336344]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.0421686407° = 168°2'30″ = 0.20987119452 rad
∠ B' = β' = 95.97991567963° = 95°58'45″ = 1.46664403542 rad
∠ C' = γ' = 95.97991567963° = 95°58'45″ = 1.46664403542 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 = 5 ; ; b = 24 ; ; c = 24 ; ;

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

p = a+b+c = 5+24+24 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-5)(26.5-24)(26.5-24) } ; ; T = sqrt{ 3560.94 } = 59.67 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 59.67 }{ 5 } = 23.87 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 59.67 }{ 24 } = 4.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 59.67 }{ 24 } = 4.97 ; ;

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{ 5**2-24**2-24**2 }{ 2 * 24 * 24 } ) = 11° 57'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-5**2-24**2 }{ 2 * 5 * 24 } ) = 84° 1'15" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-5**2-24**2 }{ 2 * 24 * 5 } ) = 84° 1'15" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 59.67 }{ 26.5 } = 2.25 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 11° 57'30" } = 12.07 ; ;




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