10 10 18 triangle

Obtuse isosceles triangle.

Sides: a = 10   b = 10   c = 18

Area: T = 39.23300904919
Perimeter: p = 38
Semiperimeter: s = 19

Angle ∠ A = α = 25.84219327632° = 25°50'31″ = 0.45110268118 rad
Angle ∠ B = β = 25.84219327632° = 25°50'31″ = 0.45110268118 rad
Angle ∠ C = γ = 128.3166134474° = 128°18'58″ = 2.243953903 rad

Height: ha = 7.84660180984
Height: hb = 7.84660180984
Height: hc = 4.35988989435

Median: ma = 13.67547943312
Median: mb = 13.67547943312
Median: mc = 4.35988989435

Inradius: r = 2.06547416048
Circumradius: R = 11.47107866935

Vertex coordinates: A[18; 0] B[0; 0] C[9; 4.35988989435]
Centroid: CG[9; 1.45329663145]
Coordinates of the circumscribed circle: U[9; -7.112188775]
Coordinates of the inscribed circle: I[9; 2.06547416048]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.1588067237° = 154°9'29″ = 0.45110268118 rad
∠ B' = β' = 154.1588067237° = 154°9'29″ = 0.45110268118 rad
∠ C' = γ' = 51.68438655263° = 51°41'2″ = 2.243953903 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 = 10 ; ; c = 18 ; ;

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

p = a+b+c = 10+10+18 = 38 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 38 }{ 2 } = 19 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19 * (19-10)(19-10)(19-18) } ; ; T = sqrt{ 1539 } = 39.23 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 39.23 }{ 10 } = 7.85 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 39.23 }{ 10 } = 7.85 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 39.23 }{ 18 } = 4.36 ; ;

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**2-10**2-18**2 }{ 2 * 10 * 18 } ) = 25° 50'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 10**2-10**2-18**2 }{ 2 * 10 * 18 } ) = 25° 50'31" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-10**2-10**2 }{ 2 * 10 * 10 } ) = 128° 18'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 39.23 }{ 19 } = 2.06 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 25° 50'31" } = 11.47 ; ;




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