18 18 23 triangle

Acute isosceles triangle.

Sides: a = 18   b = 18   c = 23

Area: T = 159.2454897877
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 50.29109834469° = 50°17'28″ = 0.87877432452 rad
Angle ∠ B = β = 50.29109834469° = 50°17'28″ = 0.87877432452 rad
Angle ∠ C = γ = 79.41880331061° = 79°25'5″ = 1.38661061632 rad

Height: ha = 17.69438775419
Height: hb = 17.69438775419
Height: hc = 13.84773824241

Median: ma = 18.58876302954
Median: mb = 18.58876302954
Median: mc = 13.84773824241

Inradius: r = 5.39881321314
Circumradius: R = 11.69989619437

Vertex coordinates: A[23; 0] B[0; 0] C[11.5; 13.84773824241]
Centroid: CG[11.5; 4.61657941414]
Coordinates of the circumscribed circle: U[11.5; 2.14884204804]
Coordinates of the inscribed circle: I[11.5; 5.39881321314]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 129.7099016553° = 129°42'32″ = 0.87877432452 rad
∠ B' = β' = 129.7099016553° = 129°42'32″ = 0.87877432452 rad
∠ C' = γ' = 100.5821966894° = 100°34'55″ = 1.38661061632 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 = 18 ; ; b = 18 ; ; c = 23 ; ;

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

p = a+b+c = 18+18+23 = 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 * (29.5-18)(29.5-18)(29.5-23) } ; ; T = sqrt{ 25358.94 } = 159.24 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 159.24 }{ 18 } = 17.69 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 159.24 }{ 18 } = 17.69 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 159.24 }{ 23 } = 13.85 ; ;

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{ 18**2-18**2-23**2 }{ 2 * 18 * 23 } ) = 50° 17'28" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-18**2-23**2 }{ 2 * 18 * 23 } ) = 50° 17'28" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-18**2-18**2 }{ 2 * 18 * 18 } ) = 79° 25'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 159.24 }{ 29.5 } = 5.4 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 50° 17'28" } = 11.7 ; ;




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