3 24 24 triangle

Acute isosceles triangle.

Sides: a = 3   b = 24   c = 24

Area: T = 35.9329618701
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 7.16766433969° = 7°10' = 0.12550815236 rad
Angle ∠ B = β = 86.41766783015° = 86°25' = 1.5088255565 rad
Angle ∠ C = γ = 86.41766783015° = 86°25' = 1.5088255565 rad

Height: ha = 23.9533079134
Height: hb = 2.99441348918
Height: hc = 2.99441348918

Median: ma = 23.9533079134
Median: mb = 12.1866057607
Median: mc = 12.1866057607

Inradius: r = 1.40990046549
Circumradius: R = 12.02435063888

Vertex coordinates: A[24; 0] B[0; 0] C[0.18875; 2.99441348918]
Centroid: CG[8.06325; 0.99880449639]
Coordinates of the circumscribed circle: U[12; 0.75114691493]
Coordinates of the inscribed circle: I[1.5; 1.40990046549]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 172.8333356603° = 172°50' = 0.12550815236 rad
∠ B' = β' = 93.58333216985° = 93°35' = 1.5088255565 rad
∠ C' = γ' = 93.58333216985° = 93°35' = 1.5088255565 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 = 3 ; ; b = 24 ; ; c = 24 ; ;

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

p = a+b+c = 3+24+24 = 51 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 51 }{ 2 } = 25.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25.5 * (25.5-3)(25.5-24)(25.5-24) } ; ; T = sqrt{ 1290.94 } = 35.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 35.93 }{ 3 } = 23.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 35.93 }{ 24 } = 2.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 35.93 }{ 24 } = 2.99 ; ;

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{ 3**2-24**2-24**2 }{ 2 * 24 * 24 } ) = 7° 10' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-3**2-24**2 }{ 2 * 3 * 24 } ) = 86° 25' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-3**2-24**2 }{ 2 * 24 * 3 } ) = 86° 25' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 35.93 }{ 25.5 } = 1.41 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 7° 10' } = 12.02 ; ;




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