17 17 27 triangle

Obtuse isosceles triangle.

Sides: a = 17   b = 17   c = 27

Area: T = 139.4821853659
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 37.4288005543° = 37°25'41″ = 0.65332419292 rad
Angle ∠ B = β = 37.4288005543° = 37°25'41″ = 0.65332419292 rad
Angle ∠ C = γ = 105.1443988914° = 105°8'38″ = 1.83551087952 rad

Height: ha = 16.41096298422
Height: hb = 16.41096298422
Height: hc = 10.33219891599

Median: ma = 20.8998564544
Median: mb = 20.8998564544
Median: mc = 10.33219891599

Inradius: r = 4.57331755298
Circumradius: R = 13.98656902445

Vertex coordinates: A[27; 0] B[0; 0] C[13.5; 10.33219891599]
Centroid: CG[13.5; 3.44439963866]
Coordinates of the circumscribed circle: U[13.5; -3.65437010846]
Coordinates of the inscribed circle: I[13.5; 4.57331755298]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.5721994457° = 142°34'19″ = 0.65332419292 rad
∠ B' = β' = 142.5721994457° = 142°34'19″ = 0.65332419292 rad
∠ C' = γ' = 74.85660110861° = 74°51'22″ = 1.83551087952 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 = 17 ; ; b = 17 ; ; c = 27 ; ;

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

p = a+b+c = 17+17+27 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-17)(30.5-17)(30.5-27) } ; ; T = sqrt{ 19455.19 } = 139.48 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 139.48 }{ 17 } = 16.41 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 139.48 }{ 17 } = 16.41 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 139.48 }{ 27 } = 10.33 ; ;

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{ 17**2+27**2-17**2 }{ 2 * 17 * 27 } ) = 37° 25'41" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 17**2+27**2-17**2 }{ 2 * 17 * 27 } ) = 37° 25'41" ; ; gamma = 180° - alpha - beta = 180° - 37° 25'41" - 37° 25'41" = 105° 8'38" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 139.48 }{ 30.5 } = 4.57 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 17 }{ 2 * sin 37° 25'41" } = 13.99 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 17**2+2 * 27**2 - 17**2 } }{ 2 } = 20.899 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 27**2+2 * 17**2 - 17**2 } }{ 2 } = 20.899 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 17**2+2 * 17**2 - 27**2 } }{ 2 } = 10.332 ; ;
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