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: h_a = 15.15769909613
Height: h_b = 15.15769909613
Height: h_c = 9.32773790531

Median: m_a = 20.05499376558
Median: m_b = 20.05499376558
Median: m_c = 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

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.

$a = 16 ; ; b = 16 ; ; c = 26 ; ;$

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

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

6. Inradius

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

7. Circumradius

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

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