6 22 22 triangle

Acute isosceles triangle.

Sides: a = 6   b = 22   c = 22

Area: T = 65.38334841531
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 15.67549595262° = 15°40'30″ = 0.27435796538 rad
Angle ∠ B = β = 82.16325202369° = 82°9'45″ = 1.43440064999 rad
Angle ∠ C = γ = 82.16325202369° = 82°9'45″ = 1.43440064999 rad

Height: ha = 21.79444947177
Height: hb = 5.94439531048
Height: hc = 5.94439531048

Median: ma = 21.79444947177
Median: mb = 11.79898261226
Median: mc = 11.79898261226

Inradius: r = 2.61553393661
Circumradius: R = 11.10437215193

Vertex coordinates: A[22; 0] B[0; 0] C[0.81881818182; 5.94439531048]
Centroid: CG[7.60660606061; 1.98113177016]
Coordinates of the circumscribed circle: U[11; 1.51441438435]
Coordinates of the inscribed circle: I[3; 2.61553393661]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.3255040474° = 164°19'30″ = 0.27435796538 rad
∠ B' = β' = 97.83774797631° = 97°50'15″ = 1.43440064999 rad
∠ C' = γ' = 97.83774797631° = 97°50'15″ = 1.43440064999 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 = 6 ; ; b = 22 ; ; c = 22 ; ;

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

p = a+b+c = 6+22+22 = 50 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 50 }{ 2 } = 25 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25 * (25-6)(25-22)(25-22) } ; ; T = sqrt{ 4275 } = 65.38 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 65.38 }{ 6 } = 21.79 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 65.38 }{ 22 } = 5.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 65.38 }{ 22 } = 5.94 ; ;

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{ 6**2-22**2-22**2 }{ 2 * 22 * 22 } ) = 15° 40'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-6**2-22**2 }{ 2 * 6 * 22 } ) = 82° 9'45" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-6**2-22**2 }{ 2 * 22 * 6 } ) = 82° 9'45" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 65.38 }{ 25 } = 2.62 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 15° 40'30" } = 11.1 ; ;




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