16 16 30 triangle

Obtuse isosceles triangle.

Sides: a = 16   b = 16   c = 30

Area: T = 83.51664654425
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 20.36441348063° = 20°21'51″ = 0.35554212017 rad
Angle ∠ B = β = 20.36441348063° = 20°21'51″ = 0.35554212017 rad
Angle ∠ C = γ = 139.2721730387° = 139°16'18″ = 2.43107502502 rad

Height: ha = 10.44395581803
Height: hb = 10.44395581803
Height: hc = 5.56877643628

Median: ma = 22.67215680975
Median: mb = 22.67215680975
Median: mc = 5.56877643628

Inradius: r = 2.69440795304
Circumradius: R = 22.98994786594

Vertex coordinates: A[30; 0] B[0; 0] C[15; 5.56877643628]
Centroid: CG[15; 1.85659214543]
Coordinates of the circumscribed circle: U[15; -17.42217142966]
Coordinates of the inscribed circle: I[15; 2.69440795304]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.6365865194° = 159°38'9″ = 0.35554212017 rad
∠ B' = β' = 159.6365865194° = 159°38'9″ = 0.35554212017 rad
∠ C' = γ' = 40.72882696126° = 40°43'42″ = 2.43107502502 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 = 16 ; ; c = 30 ; ;

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

p = a+b+c = 16+16+30 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-16)(31-16)(31-30) } ; ; T = sqrt{ 6975 } = 83.52 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 83.52 }{ 16 } = 10.44 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 83.52 }{ 16 } = 10.44 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 83.52 }{ 30 } = 5.57 ; ;

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**2-16**2-30**2 }{ 2 * 16 * 30 } ) = 20° 21'51" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-16**2-30**2 }{ 2 * 16 * 30 } ) = 20° 21'51" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-16**2-16**2 }{ 2 * 16 * 16 } ) = 139° 16'18" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 83.52 }{ 31 } = 2.69 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 20° 21'51" } = 22.99 ; ;




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