11 29 29 triangle

Acute isosceles triangle.

Sides: a = 11   b = 29   c = 29

Area: T = 156.6055196274
Perimeter: p = 69
Semiperimeter: s = 34.5

Angle ∠ A = α = 21.86553222896° = 21°51'55″ = 0.3821621866 rad
Angle ∠ B = β = 79.06773388552° = 79°4'2″ = 1.38799853938 rad
Angle ∠ C = γ = 79.06773388552° = 79°4'2″ = 1.38799853938 rad

Height: ha = 28.47436720498
Height: hb = 10.88003583637
Height: hc = 10.88003583637

Median: ma = 28.47436720498
Median: mb = 16.45444826719
Median: mc = 16.45444826719

Inradius: r = 4.53992810514
Circumradius: R = 14.76880284884

Vertex coordinates: A[29; 0] B[0; 0] C[2.08662068966; 10.88003583637]
Centroid: CG[10.36220689655; 3.66001194546]
Coordinates of the circumscribed circle: U[14.5; 2.80108329892]
Coordinates of the inscribed circle: I[5.5; 4.53992810514]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.135467771° = 158°8'5″ = 0.3821621866 rad
∠ B' = β' = 100.9332661145° = 100°55'58″ = 1.38799853938 rad
∠ C' = γ' = 100.9332661145° = 100°55'58″ = 1.38799853938 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 = 11 ; ; b = 29 ; ; c = 29 ; ;

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

p = a+b+c = 11+29+29 = 69 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 69 }{ 2 } = 34.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34.5 * (34.5-11)(34.5-29)(34.5-29) } ; ; T = sqrt{ 24525.19 } = 156.61 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 156.61 }{ 11 } = 28.47 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 156.61 }{ 29 } = 10.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 156.61 }{ 29 } = 10.8 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 29**2+29**2-11**2 }{ 2 * 29 * 29 } ) = 21° 51'55" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 11**2+29**2-29**2 }{ 2 * 11 * 29 } ) = 79° 4'2" ; ; gamma = 180° - alpha - beta = 180° - 21° 51'55" - 79° 4'2" = 79° 4'2" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 156.61 }{ 34.5 } = 4.54 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 11 }{ 2 * sin 21° 51'55" } = 14.77 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 29**2+2 * 29**2 - 11**2 } }{ 2 } = 28.474 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 29**2+2 * 11**2 - 29**2 } }{ 2 } = 16.454 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 29**2+2 * 11**2 - 29**2 } }{ 2 } = 16.454 ; ;
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