9 16 16 triangle

Acute isosceles triangle.

Sides: a = 9   b = 16   c = 16

Area: T = 69.09436863975
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 32.67696455614° = 32°40'11″ = 0.57701928805 rad
Angle ∠ B = β = 73.66551772193° = 73°39'55″ = 1.28656998865 rad
Angle ∠ C = γ = 73.66551772193° = 73°39'55″ = 1.28656998865 rad

Height: ha = 15.35441525328
Height: hb = 8.63767107997
Height: hc = 8.63767107997

Median: ma = 15.35441525328
Median: mb = 10.22325241501
Median: mc = 10.22325241501

Inradius: r = 3.37704237267
Circumradius: R = 8.33765069955

Vertex coordinates: A[16; 0] B[0; 0] C[2.531125; 8.63767107997]
Centroid: CG[6.17770833333; 2.87989035999]
Coordinates of the circumscribed circle: U[8; 2.34546425925]
Coordinates of the inscribed circle: I[4.5; 3.37704237267]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.3330354439° = 147°19'49″ = 0.57701928805 rad
∠ B' = β' = 106.3354822781° = 106°20'5″ = 1.28656998865 rad
∠ C' = γ' = 106.3354822781° = 106°20'5″ = 1.28656998865 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 = 9 ; ; b = 16 ; ; c = 16 ; ;

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

p = a+b+c = 9+16+16 = 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 * (20.5-9)(20.5-16)(20.5-16) } ; ; T = sqrt{ 4773.94 } = 69.09 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 69.09 }{ 9 } = 15.35 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 69.09 }{ 16 } = 8.64 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 69.09 }{ 16 } = 8.64 ; ;

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{ 9**2-16**2-16**2 }{ 2 * 16 * 16 } ) = 32° 40'11" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-9**2-16**2 }{ 2 * 9 * 16 } ) = 73° 39'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-9**2-16**2 }{ 2 * 16 * 9 } ) = 73° 39'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 69.09 }{ 20.5 } = 3.37 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 32° 40'11" } = 8.34 ; ;




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