16 30 30 triangle

Acute isosceles triangle.

Sides: a = 16   b = 30   c = 30

Area: T = 231.3099316717
Perimeter: p = 76
Semiperimeter: s = 38

Angle ∠ A = α = 30.93220199068° = 30°55'55″ = 0.54398655917 rad
Angle ∠ B = β = 74.53439900466° = 74°32'2″ = 1.3010863531 rad
Angle ∠ C = γ = 74.53439900466° = 74°32'2″ = 1.3010863531 rad

Height: ha = 28.91436645896
Height: hb = 15.42106211145
Height: hc = 15.42106211145

Median: ma = 28.91436645896
Median: mb = 18.78882942281
Median: mc = 18.78882942281

Inradius: r = 6.0877087282
Circumradius: R = 15.5643575437

Vertex coordinates: A[30; 0] B[0; 0] C[4.26766666667; 15.42106211145]
Centroid: CG[11.42222222222; 5.14402070382]
Coordinates of the circumscribed circle: U[15; 4.15502867832]
Coordinates of the inscribed circle: I[8; 6.0877087282]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.0687980093° = 149°4'5″ = 0.54398655917 rad
∠ B' = β' = 105.4666009953° = 105°27'58″ = 1.3010863531 rad
∠ C' = γ' = 105.4666009953° = 105°27'58″ = 1.3010863531 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 = 16 ; ; b = 30 ; ; c = 30 ; ;

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

p = a+b+c = 16+30+30 = 76 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 76 }{ 2 } = 38 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 38 * (38-16)(38-30)(38-30) } ; ; T = sqrt{ 53504 } = 231.31 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 231.31 }{ 16 } = 28.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 231.31 }{ 30 } = 15.42 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 231.31 }{ 30 } = 15.42 ; ;

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{ 16**2-30**2-30**2 }{ 2 * 30 * 30 } ) = 30° 55'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 30**2-16**2-30**2 }{ 2 * 16 * 30 } ) = 74° 32'2" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-16**2-30**2 }{ 2 * 30 * 16 } ) = 74° 32'2" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 231.31 }{ 38 } = 6.09 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 30° 55'55" } = 15.56 ; ;




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