7 22 22 triangle

Acute isosceles triangle.

Sides: a = 7   b = 22   c = 22

Area: T = 76.01993232014
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 18.30882665693° = 18°18'30″ = 0.3219539532 rad
Angle ∠ B = β = 80.84658667154° = 80°50'45″ = 1.41110265608 rad
Angle ∠ C = γ = 80.84658667154° = 80°50'45″ = 1.41110265608 rad

Height: ha = 21.7219806629
Height: hb = 6.91108475638
Height: hc = 6.91108475638

Median: ma = 21.7219806629
Median: mb = 12.06223380818
Median: mc = 12.06223380818

Inradius: r = 2.98111499295
Circumradius: R = 11.14219039835

Vertex coordinates: A[22; 0] B[0; 0] C[1.11436363636; 6.91108475638]
Centroid: CG[7.70545454545; 2.30436158546]
Coordinates of the circumscribed circle: U[11; 1.77325756337]
Coordinates of the inscribed circle: I[3.5; 2.98111499295]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.6921733431° = 161°41'30″ = 0.3219539532 rad
∠ B' = β' = 99.15441332846° = 99°9'15″ = 1.41110265608 rad
∠ C' = γ' = 99.15441332846° = 99°9'15″ = 1.41110265608 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 = 7 ; ; b = 22 ; ; c = 22 ; ;

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

p = a+b+c = 7+22+22 = 51 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 51 }{ 2 } = 25.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25.5 * (25.5-7)(25.5-22)(25.5-22) } ; ; T = sqrt{ 5778.94 } = 76.02 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 76.02 }{ 7 } = 21.72 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 76.02 }{ 22 } = 6.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 76.02 }{ 22 } = 6.91 ; ;

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{ 7**2-22**2-22**2 }{ 2 * 22 * 22 } ) = 18° 18'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-7**2-22**2 }{ 2 * 7 * 22 } ) = 80° 50'45" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-7**2-22**2 }{ 2 * 22 * 7 } ) = 80° 50'45" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 76.02 }{ 25.5 } = 2.98 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 18° 18'30" } = 11.14 ; ;




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