12 12 17 triangle

Obtuse isosceles triangle.

Sides: a = 12   b = 12   c = 17

Area: T = 721.9995659709
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 44.90105279607° = 44°54'2″ = 0.78436620488 rad
Angle ∠ B = β = 44.90105279607° = 44°54'2″ = 0.78436620488 rad
Angle ∠ C = γ = 90.19989440786° = 90°11'56″ = 1.5744268556 rad

Height: ha = 121.9999276618
Height: hb = 121.9999276618
Height: hc = 8.4710537173

Median: ma = 13.43550288425
Median: mb = 13.43550288425
Median: mc = 8.4710537173

Inradius: r = 3.51221739498
Circumradius: R = 8.55000512399

Vertex coordinates: A[17; 0] B[0; 0] C[8.5; 8.4710537173]
Centroid: CG[8.5; 2.8243512391]
Coordinates of the circumscribed circle: U[8.5; -0.03295140668]
Coordinates of the inscribed circle: I[8.5; 3.51221739498]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.0999472039° = 135°5'58″ = 0.78436620488 rad
∠ B' = β' = 135.0999472039° = 135°5'58″ = 0.78436620488 rad
∠ C' = γ' = 89.80110559214° = 89°48'4″ = 1.5744268556 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 = 12 ; ; b = 12 ; ; c = 17 ; ;

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

p = a+b+c = 12+12+17 = 41 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 41 }{ 2 } = 20.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.5 * (20.5-12)(20.5-12)(20.5-17) } ; ; T = sqrt{ 5183.94 } = 72 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 72 }{ 12 } = 12 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 72 }{ 12 } = 12 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 72 }{ 17 } = 8.47 ; ;

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{ 12**2-12**2-17**2 }{ 2 * 12 * 17 } ) = 44° 54'2" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-12**2-17**2 }{ 2 * 12 * 17 } ) = 44° 54'2" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-12**2-12**2 }{ 2 * 12 * 12 } ) = 90° 11'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 72 }{ 20.5 } = 3.51 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 44° 54'2" } = 8.5 ; ;




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