3 16 16 triangle

Acute isosceles triangle.

Sides: a = 3   b = 16   c = 16

Area: T = 23.89442984831
Perimeter: p = 35
Semiperimeter: s = 17.5

Angle ∠ A = α = 10.75987579822° = 10°45'32″ = 0.18877757502 rad
Angle ∠ B = β = 84.62106210089° = 84°37'14″ = 1.47769084517 rad
Angle ∠ C = γ = 84.62106210089° = 84°37'14″ = 1.47769084517 rad

Height: ha = 15.93295323221
Height: hb = 2.98767873104
Height: hc = 2.98767873104

Median: ma = 15.93295323221
Median: mb = 8.27664726786
Median: mc = 8.27664726786

Inradius: r = 1.36553884847
Circumradius: R = 8.03553897034

Vertex coordinates: A[16; 0] B[0; 0] C[0.281125; 2.98767873104]
Centroid: CG[5.42770833333; 0.99655957701]
Coordinates of the circumscribed circle: U[8; 0.75333177847]
Coordinates of the inscribed circle: I[1.5; 1.36553884847]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.2411242018° = 169°14'28″ = 0.18877757502 rad
∠ B' = β' = 95.37993789911° = 95°22'46″ = 1.47769084517 rad
∠ C' = γ' = 95.37993789911° = 95°22'46″ = 1.47769084517 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 = 3 ; ; b = 16 ; ; c = 16 ; ;

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

p = a+b+c = 3+16+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 * (17.5-3)(17.5-16)(17.5-16) } ; ; T = sqrt{ 570.94 } = 23.89 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 23.89 }{ 3 } = 15.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 23.89 }{ 16 } = 2.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 23.89 }{ 16 } = 2.99 ; ;

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{ 3**2-16**2-16**2 }{ 2 * 16 * 16 } ) = 10° 45'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-3**2-16**2 }{ 2 * 3 * 16 } ) = 84° 37'14" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-3**2-16**2 }{ 2 * 16 * 3 } ) = 84° 37'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 23.89 }{ 17.5 } = 1.37 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 10° 45'32" } = 8.04 ; ;




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