10 18 18 triangle

Acute isosceles triangle.

Sides: a = 10   b = 18   c = 18

Area: T = 86.4588082329
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 32.25552404263° = 32°15'19″ = 0.56329601465 rad
Angle ∠ B = β = 73.87223797868° = 73°52'21″ = 1.28993162536 rad
Angle ∠ C = γ = 73.87223797868° = 73°52'21″ = 1.28993162536 rad

Height: ha = 17.29216164658
Height: hb = 9.60664535921
Height: hc = 9.60664535921

Median: ma = 17.29216164658
Median: mb = 11.44655231423
Median: mc = 11.44655231423

Inradius: r = 3.75990470578
Circumradius: R = 9.36987018979

Vertex coordinates: A[18; 0] B[0; 0] C[2.77877777778; 9.60664535921]
Centroid: CG[6.92659259259; 3.20221511974]
Coordinates of the circumscribed circle: U[9; 2.60224171938]
Coordinates of the inscribed circle: I[5; 3.75990470578]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.7454759574° = 147°44'41″ = 0.56329601465 rad
∠ B' = β' = 106.1287620213° = 106°7'39″ = 1.28993162536 rad
∠ C' = γ' = 106.1287620213° = 106°7'39″ = 1.28993162536 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 = 10 ; ; b = 18 ; ; c = 18 ; ;

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

p = a+b+c = 10+18+18 = 46 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 46 }{ 2 } = 23 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23 * (23-10)(23-18)(23-18) } ; ; T = sqrt{ 7475 } = 86.46 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 86.46 }{ 10 } = 17.29 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 86.46 }{ 18 } = 9.61 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 86.46 }{ 18 } = 9.61 ; ;

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{ 10**2-18**2-18**2 }{ 2 * 18 * 18 } ) = 32° 15'19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-10**2-18**2 }{ 2 * 10 * 18 } ) = 73° 52'21" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-10**2-18**2 }{ 2 * 18 * 10 } ) = 73° 52'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 86.46 }{ 23 } = 3.76 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 32° 15'19" } = 9.37 ; ;




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