12 18 18 triangle

Acute isosceles triangle.

Sides: a = 12   b = 18   c = 18

Area: T = 101.8233376491
Perimeter: p = 48
Semiperimeter: s = 24

Angle ∠ A = α = 38.9422441269° = 38°56'33″ = 0.68796738189 rad
Angle ∠ B = β = 70.52987793655° = 70°31'44″ = 1.23109594173 rad
Angle ∠ C = γ = 70.52987793655° = 70°31'44″ = 1.23109594173 rad

Height: ha = 16.97105627485
Height: hb = 11.3143708499
Height: hc = 11.3143708499

Median: ma = 16.97105627485
Median: mb = 12.36993168769
Median: mc = 12.36993168769

Inradius: r = 4.24326406871
Circumradius: R = 9.5465941546

Vertex coordinates: A[18; 0] B[0; 0] C[4; 11.3143708499]
Centroid: CG[7.33333333333; 3.77112361663]
Coordinates of the circumscribed circle: U[9; 3.18219805153]
Coordinates of the inscribed circle: I[6; 4.24326406871]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.0587558731° = 141°3'27″ = 0.68796738189 rad
∠ B' = β' = 109.4711220634° = 109°28'16″ = 1.23109594173 rad
∠ C' = γ' = 109.4711220634° = 109°28'16″ = 1.23109594173 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 = 12 ; ; b = 18 ; ; c = 18 ; ;

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

p = a+b+c = 12+18+18 = 48 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 48 }{ 2 } = 24 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24 * (24-12)(24-18)(24-18) } ; ; T = sqrt{ 10368 } = 101.82 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 101.82 }{ 12 } = 16.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 101.82 }{ 18 } = 11.31 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 101.82 }{ 18 } = 11.31 ; ;

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{ 12**2-18**2-18**2 }{ 2 * 18 * 18 } ) = 38° 56'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-12**2-18**2 }{ 2 * 12 * 18 } ) = 70° 31'44" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-12**2-18**2 }{ 2 * 18 * 12 } ) = 70° 31'44" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 101.82 }{ 24 } = 4.24 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 38° 56'33" } = 9.55 ; ;




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