15 15 22 triangle

Obtuse isosceles triangle.

Sides: a = 15   b = 15   c = 22

Area: T = 112.1788429299
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 42.83334280661° = 42°50' = 0.74875843497 rad
Angle ∠ B = β = 42.83334280661° = 42°50' = 0.74875843497 rad
Angle ∠ C = γ = 94.33331438679° = 94°19'59″ = 1.64664239543 rad

Height: ha = 14.95771239065
Height: hb = 14.95771239065
Height: hc = 10.19880390272

Median: ma = 17.27699160392
Median: mb = 17.27699160392
Median: mc = 10.19880390272

Inradius: r = 4.3154554973
Circumradius: R = 11.03215326015

Vertex coordinates: A[22; 0] B[0; 0] C[11; 10.19880390272]
Centroid: CG[11; 3.39993463424]
Coordinates of the circumscribed circle: U[11; -0.83334935743]
Coordinates of the inscribed circle: I[11; 4.3154554973]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.1676571934° = 137°10' = 0.74875843497 rad
∠ B' = β' = 137.1676571934° = 137°10' = 0.74875843497 rad
∠ C' = γ' = 85.66768561321° = 85°40'1″ = 1.64664239543 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 = 15 ; ; b = 15 ; ; c = 22 ; ;

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

p = a+b+c = 15+15+22 = 52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 52 }{ 2 } = 26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26 * (26-15)(26-15)(26-22) } ; ; T = sqrt{ 12584 } = 112.18 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 112.18 }{ 15 } = 14.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 112.18 }{ 15 } = 14.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 112.18 }{ 22 } = 10.2 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 15**2+22**2-15**2 }{ 2 * 15 * 22 } ) = 42° 50' ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 15**2+22**2-15**2 }{ 2 * 15 * 22 } ) = 42° 50' ; ; gamma = 180° - alpha - beta = 180° - 42° 50' - 42° 50' = 94° 19'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 112.18 }{ 26 } = 4.31 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 15 }{ 2 * sin 42° 50' } = 11.03 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 15**2+2 * 22**2 - 15**2 } }{ 2 } = 17.27 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 22**2+2 * 15**2 - 15**2 } }{ 2 } = 17.27 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 15**2+2 * 15**2 - 22**2 } }{ 2 } = 10.198 ; ;
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