11 18 18 triangle

Acute isosceles triangle.

Sides: a = 11   b = 18   c = 18

Area: T = 94.26552507555
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 35.5833181146° = 35°34'59″ = 0.62110436693 rad
Angle ∠ B = β = 72.2088409427° = 72°12'30″ = 1.26602744921 rad
Angle ∠ C = γ = 72.2088409427° = 72°12'30″ = 1.26602744921 rad

Height: ha = 17.1399136501
Height: hb = 10.47439167506
Height: hc = 10.47439167506

Median: ma = 17.1399136501
Median: mb = 11.89553772534
Median: mc = 11.89553772534

Inradius: r = 4.01112872662
Circumradius: R = 9.45220514491

Vertex coordinates: A[18; 0] B[0; 0] C[3.36111111111; 10.47439167506]
Centroid: CG[7.12203703704; 3.49113055835]
Coordinates of the circumscribed circle: U[9; 2.88881268317]
Coordinates of the inscribed circle: I[5.5; 4.01112872662]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.4176818854° = 144°25'1″ = 0.62110436693 rad
∠ B' = β' = 107.7921590573° = 107°47'30″ = 1.26602744921 rad
∠ C' = γ' = 107.7921590573° = 107°47'30″ = 1.26602744921 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 = 11 ; ; b = 18 ; ; c = 18 ; ;

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

p = a+b+c = 11+18+18 = 47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 47 }{ 2 } = 23.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23.5 * (23.5-11)(23.5-18)(23.5-18) } ; ; T = sqrt{ 8885.94 } = 94.27 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 94.27 }{ 11 } = 17.14 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 94.27 }{ 18 } = 10.47 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 94.27 }{ 18 } = 10.47 ; ;

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{ 11**2-18**2-18**2 }{ 2 * 18 * 18 } ) = 35° 34'59" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-11**2-18**2 }{ 2 * 11 * 18 } ) = 72° 12'30" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-11**2-18**2 }{ 2 * 18 * 11 } ) = 72° 12'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 94.27 }{ 23.5 } = 4.01 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 35° 34'59" } = 9.45 ; ;




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