13 16 16 triangle

Acute isosceles triangle.

Sides: a = 13   b = 16   c = 16

Area: T = 95.03112448619
Perimeter: p = 45
Semiperimeter: s = 22.5

Angle ∠ A = α = 47.93989646355° = 47°56'20″ = 0.83766927729 rad
Angle ∠ B = β = 66.03105176822° = 66°1'50″ = 1.15224499404 rad
Angle ∠ C = γ = 66.03105176822° = 66°1'50″ = 1.15224499404 rad

Height: ha = 14.62201915172
Height: hb = 11.87989056077
Height: hc = 11.87989056077

Median: ma = 14.62201915172
Median: mb = 12.1866057607
Median: mc = 12.1866057607

Inradius: r = 4.22436108828
Circumradius: R = 8.75550152711

Vertex coordinates: A[16; 0] B[0; 0] C[5.281125; 11.87989056077]
Centroid: CG[7.094375; 3.96596352026]
Coordinates of the circumscribed circle: U[8; 3.55767249539]
Coordinates of the inscribed circle: I[6.5; 4.22436108828]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.0611035364° = 132°3'40″ = 0.83766927729 rad
∠ B' = β' = 113.9699482318° = 113°58'10″ = 1.15224499404 rad
∠ C' = γ' = 113.9699482318° = 113°58'10″ = 1.15224499404 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 = 13 ; ; b = 16 ; ; c = 16 ; ;

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

p = a+b+c = 13+16+16 = 45 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 45 }{ 2 } = 22.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22.5 * (22.5-13)(22.5-16)(22.5-16) } ; ; T = sqrt{ 9030.94 } = 95.03 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 95.03 }{ 13 } = 14.62 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 95.03 }{ 16 } = 11.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 95.03 }{ 16 } = 11.88 ; ;

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{ 13**2-16**2-16**2 }{ 2 * 16 * 16 } ) = 47° 56'20" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-13**2-16**2 }{ 2 * 13 * 16 } ) = 66° 1'50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-13**2-16**2 }{ 2 * 16 * 13 } ) = 66° 1'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 95.03 }{ 22.5 } = 4.22 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 47° 56'20" } = 8.76 ; ;




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