8 11 16 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 11   c = 16

Area: T = 40.26108680979
Perimeter: p = 35
Semiperimeter: s = 17.5

Angle ∠ A = α = 27.227653999° = 27°13'36″ = 0.47551927668 rad
Angle ∠ B = β = 38.98219890646° = 38°58'55″ = 0.68803640582 rad
Angle ∠ C = γ = 113.7911470945° = 113°47'29″ = 1.98660358287 rad

Height: ha = 10.06552170245
Height: hb = 7.3220157836
Height: hc = 5.03326085122

Median: ma = 13.13439255366
Median: mb = 11.39107857499
Median: mc = 5.3398539126

Inradius: r = 2.30106210342
Circumradius: R = 8.74329808802

Vertex coordinates: A[16; 0] B[0; 0] C[6.219875; 5.03326085122]
Centroid: CG[7.406625; 1.67875361707]
Coordinates of the circumscribed circle: U[8; -3.52769979687]
Coordinates of the inscribed circle: I[6.5; 2.30106210342]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.773346001° = 152°46'24″ = 0.47551927668 rad
∠ B' = β' = 141.0188010935° = 141°1'5″ = 0.68803640582 rad
∠ C' = γ' = 66.20985290545° = 66°12'31″ = 1.98660358287 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 = 8 ; ; b = 11 ; ; c = 16 ; ;

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

p = a+b+c = 8+11+16 = 35 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 35 }{ 2 } = 17.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17.5 * (17.5-8)(17.5-11)(17.5-16) } ; ; T = sqrt{ 1620.94 } = 40.26 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 40.26 }{ 8 } = 10.07 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 40.26 }{ 11 } = 7.32 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 40.26 }{ 16 } = 5.03 ; ;

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{ 8**2-11**2-16**2 }{ 2 * 11 * 16 } ) = 27° 13'36" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-8**2-16**2 }{ 2 * 8 * 16 } ) = 38° 58'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-8**2-11**2 }{ 2 * 11 * 8 } ) = 113° 47'29" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 40.26 }{ 17.5 } = 2.3 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 27° 13'36" } = 8.74 ; ;




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