11 28 28 triangle

Acute isosceles triangle.

Sides: a = 11   b = 28   c = 28

Area: T = 1510.999793046
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 22.65663777041° = 22°39'23″ = 0.39554283875 rad
Angle ∠ B = β = 78.67218111479° = 78°40'19″ = 1.3733082133 rad
Angle ∠ C = γ = 78.67218111479° = 78°40'19″ = 1.3733082133 rad

Height: ha = 27.45545078266
Height: hb = 10.78656995033
Height: hc = 10.78656995033

Median: ma = 27.45545078266
Median: mb = 16.0165617378
Median: mc = 16.0165617378

Inradius: r = 4.50774565088
Circumradius: R = 14.27881652644

Vertex coordinates: A[28; 0] B[0; 0] C[2.16107142857; 10.78656995033]
Centroid: CG[10.05435714286; 3.59552331678]
Coordinates of the circumscribed circle: U[14; 2.80546396055]
Coordinates of the inscribed circle: I[5.5; 4.50774565088]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.3443622296° = 157°20'37″ = 0.39554283875 rad
∠ B' = β' = 101.3288188852° = 101°19'41″ = 1.3733082133 rad
∠ C' = γ' = 101.3288188852° = 101°19'41″ = 1.3733082133 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 = 28 ; ; c = 28 ; ;

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

p = a+b+c = 11+28+28 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-11)(33.5-28)(33.5-28) } ; ; T = sqrt{ 22800.94 } = 151 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 151 }{ 11 } = 27.45 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 151 }{ 28 } = 10.79 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 151 }{ 28 } = 10.79 ; ;

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{ 11**2-28**2-28**2 }{ 2 * 28 * 28 } ) = 22° 39'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-11**2-28**2 }{ 2 * 11 * 28 } ) = 78° 40'19" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-11**2-28**2 }{ 2 * 28 * 11 } ) = 78° 40'19" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 151 }{ 33.5 } = 4.51 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 22° 39'23" } = 14.28 ; ;




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