16 16 26 triangle

Obtuse isosceles triangle.

Sides: a = 16   b = 16   c = 26

Area: T = 121.256592769
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 35.65990876961° = 35°39'33″ = 0.62223684886 rad
Angle ∠ B = β = 35.65990876961° = 35°39'33″ = 0.62223684886 rad
Angle ∠ C = γ = 108.6821824608° = 108°40'55″ = 1.89768556765 rad

Height: ha = 15.15769909613
Height: hb = 15.15769909613
Height: hc = 9.32773790531

Median: ma = 20.05499376558
Median: mb = 20.05499376558
Median: mc = 9.32773790531

Inradius: r = 4.18112388859
Circumradius: R = 13.72330404459

Vertex coordinates: A[26; 0] B[0; 0] C[13; 9.32773790531]
Centroid: CG[13; 3.1099126351]
Coordinates of the circumscribed circle: U[13; -4.39656613928]
Coordinates of the inscribed circle: I[13; 4.18112388859]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.3410912304° = 144°20'27″ = 0.62223684886 rad
∠ B' = β' = 144.3410912304° = 144°20'27″ = 0.62223684886 rad
∠ C' = γ' = 71.31881753923° = 71°19'5″ = 1.89768556765 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 = 16 ; ; b = 16 ; ; c = 26 ; ;

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

p = a+b+c = 16+16+26 = 58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 58 }{ 2 } = 29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29 * (29-16)(29-16)(29-26) } ; ; T = sqrt{ 14703 } = 121.26 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 121.26 }{ 16 } = 15.16 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 121.26 }{ 16 } = 15.16 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 121.26 }{ 26 } = 9.33 ; ;

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{ 16**2+26**2-16**2 }{ 2 * 16 * 26 } ) = 35° 39'33" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 16**2+26**2-16**2 }{ 2 * 16 * 26 } ) = 35° 39'33" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 16**2+16**2-26**2 }{ 2 * 16 * 16 } ) = 108° 40'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 121.26 }{ 29 } = 4.18 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 35° 39'33" } = 13.72 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 26**2 - 16**2 } }{ 2 } = 20.05 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 16**2 - 16**2 } }{ 2 } = 20.05 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 16**2 - 26**2 } }{ 2 } = 9.327 ; ;
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