7 24 24 triangle

Acute isosceles triangle.

Sides: a = 7   b = 24   c = 24

Area: T = 83.10219704941
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 16.77110772942° = 16°46'16″ = 0.29327105179 rad
Angle ∠ B = β = 81.61444613529° = 81°36'52″ = 1.42444410679 rad
Angle ∠ C = γ = 81.61444613529° = 81°36'52″ = 1.42444410679 rad

Height: ha = 23.74334201412
Height: hb = 6.92551642078
Height: hc = 6.92551642078

Median: ma = 23.74334201412
Median: mb = 12.98107549857
Median: mc = 12.98107549857

Inradius: r = 3.02218898361
Circumradius: R = 12.13296762761

Vertex coordinates: A[24; 0] B[0; 0] C[1.02108333333; 6.92551642078]
Centroid: CG[8.34402777778; 2.30883880693]
Coordinates of the circumscribed circle: U[12; 1.76989111236]
Coordinates of the inscribed circle: I[3.5; 3.02218898361]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.2298922706° = 163°13'44″ = 0.29327105179 rad
∠ B' = β' = 98.38655386471° = 98°23'8″ = 1.42444410679 rad
∠ C' = γ' = 98.38655386471° = 98°23'8″ = 1.42444410679 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 = 7 ; ; b = 24 ; ; c = 24 ; ;

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

p = a+b+c = 7+24+24 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-7)(27.5-24)(27.5-24) } ; ; T = sqrt{ 6905.94 } = 83.1 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 83.1 }{ 7 } = 23.74 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 83.1 }{ 24 } = 6.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 83.1 }{ 24 } = 6.93 ; ;

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{ 7**2-24**2-24**2 }{ 2 * 24 * 24 } ) = 16° 46'16" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-7**2-24**2 }{ 2 * 7 * 24 } ) = 81° 36'52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-7**2-24**2 }{ 2 * 24 * 7 } ) = 81° 36'52" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 83.1 }{ 27.5 } = 3.02 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 16° 46'16" } = 12.13 ; ;




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