13 13 22 triangle

Obtuse isosceles triangle.

Sides: a = 13 b = 13 c = 22

Area: T = 76.2110235533
Perimeter: p = 48
Semiperimeter: s = 24

Angle ∠ A = α = 32.2044227504° = 32°12'15″ = 0.5622069803 rad
Angle ∠ B = β = 32.2044227504° = 32°12'15″ = 0.5622069803 rad
Angle ∠ C = γ = 115.5921544992° = 115°35'30″ = 2.01774530476 rad

Height: h_a = 11.72546516205
Height: h_b = 11.72546516205
Height: h_c = 6.92882032303

Median: m_a = 16.86597153001
Median: m_b = 16.86597153001
Median: m_c = 6.92882032303

Inradius: r = 3.17554264805
Circumradius: R = 12.19765244366

Vertex coordinates: A[22; 0] B[0; 0] C[11; 6.92882032303]
Centroid: CG[11; 2.30994010768]
Coordinates of the circumscribed circle: U[11; -5.26883212064]
Coordinates of the inscribed circle: I[11; 3.17554264805]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.7965772496° = 147°47'45″ = 0.5622069803 rad
∠ B' = β' = 147.7965772496° = 147°47'45″ = 0.5622069803 rad
∠ C' = γ' = 64.40884550079° = 64°24'30″ = 2.01774530476 rad

Calculate another triangle

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.

$a = 13 ; ; b = 13 ; ; c = 22 ; ;$

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

$p = a+b+c = 13+13+22 = 48 ; ;$

2. Semiperimeter of the triangle

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

3. The triangle area using Heron's formula

$T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24 * (24-13)(24-13)(24-22) } ; ; T = sqrt{ 5808 } = 76.21 ; ;$

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

$T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 76.21 }{ 13 } = 11.72 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 76.21 }{ 13 } = 11.72 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 76.21 }{ 22 } = 6.93 ; ;$

5. Calculation of the inner angles of the triangle using a Law of Cosines

$a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 13**2-13**2-22**2 }{ 2 * 13 * 22 } ) = 32° 12'15" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-13**2-22**2 }{ 2 * 13 * 22 } ) = 32° 12'15" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-13**2-13**2 }{ 2 * 13 * 13 } ) = 115° 35'30" ; ;$

6. Inradius

$T = rs ; ; r = fraction{ T }{ s } = fraction{ 76.21 }{ 24 } = 3.18 ; ;$

7. Circumradius

$R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 32° 12'15" } = 12.2 ; ;$

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