9 9 16 triangle

Obtuse isosceles triangle.

Sides: a = 9   b = 9   c = 16

Area: T = 32.98548450049
Perimeter: p = 34
Semiperimeter: s = 17

Angle ∠ A = α = 27.26660444507° = 27°15'58″ = 0.47658822497 rad
Angle ∠ B = β = 27.26660444507° = 27°15'58″ = 0.47658822497 rad
Angle ∠ C = γ = 125.4687911099° = 125°28'4″ = 2.19898281543 rad

Height: ha = 7.33299655567
Height: hb = 7.33299655567
Height: hc = 4.12331056256

Median: ma = 12.17657956619
Median: mb = 12.17657956619
Median: mc = 4.12331056256

Inradius: r = 1.94402850003
Circumradius: R = 9.8232692814

Vertex coordinates: A[16; 0] B[0; 0] C[8; 4.12331056256]
Centroid: CG[8; 1.37443685419]
Coordinates of the circumscribed circle: U[8; -5.76995871884]
Coordinates of the inscribed circle: I[8; 1.94402850003]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.7343955549° = 152°44'2″ = 0.47658822497 rad
∠ B' = β' = 152.7343955549° = 152°44'2″ = 0.47658822497 rad
∠ C' = γ' = 54.53220889015° = 54°31'56″ = 2.19898281543 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 = 9 ; ; c = 16 ; ;

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

p = a+b+c = 9+9+16 = 34 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 34 }{ 2 } = 17 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17 * (17-9)(17-9)(17-16) } ; ; T = sqrt{ 1088 } = 32.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 32.98 }{ 9 } = 7.33 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 32.98 }{ 9 } = 7.33 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 32.98 }{ 16 } = 4.12 ; ;

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**2-9**2-16**2 }{ 2 * 9 * 16 } ) = 27° 15'58" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 9**2-9**2-16**2 }{ 2 * 9 * 16 } ) = 27° 15'58" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-9**2-9**2 }{ 2 * 9 * 9 } ) = 125° 28'4" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 32.98 }{ 17 } = 1.94 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 27° 15'58" } = 9.82 ; ;




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