17 22 22 triangle

Acute isosceles triangle.

Sides: a = 17   b = 22   c = 22

Area: T = 172.4798803046
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 45.4576845195° = 45°27'25″ = 0.79333716162 rad
Angle ∠ B = β = 67.27215774025° = 67°16'18″ = 1.17441105187 rad
Angle ∠ C = γ = 67.27215774025° = 67°16'18″ = 1.17441105187 rad

Height: ha = 20.29216238877
Height: hb = 15.6879891186
Height: hc = 15.6879891186

Median: ma = 20.29216238877
Median: mb = 16.29441707368
Median: mc = 16.29441707368

Inradius: r = 5.65550427228
Circumradius: R = 11.92661031714

Vertex coordinates: A[22; 0] B[0; 0] C[6.56881818182; 15.6879891186]
Centroid: CG[9.52327272727; 5.22766303953]
Coordinates of the circumscribed circle: U[11; 4.6087812589]
Coordinates of the inscribed circle: I[8.5; 5.65550427228]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.5433154805° = 134°32'35″ = 0.79333716162 rad
∠ B' = β' = 112.7288422598° = 112°43'42″ = 1.17441105187 rad
∠ C' = γ' = 112.7288422598° = 112°43'42″ = 1.17441105187 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 = 17 ; ; b = 22 ; ; c = 22 ; ;

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

p = a+b+c = 17+22+22 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-17)(30.5-22)(30.5-22) } ; ; T = sqrt{ 29748.94 } = 172.48 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 172.48 }{ 17 } = 20.29 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 172.48 }{ 22 } = 15.68 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 172.48 }{ 22 } = 15.68 ; ;

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{ 22**2+22**2-17**2 }{ 2 * 22 * 22 } ) = 45° 27'25" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 17**2+22**2-22**2 }{ 2 * 17 * 22 } ) = 67° 16'18" ; ; gamma = 180° - alpha - beta = 180° - 45° 27'25" - 67° 16'18" = 67° 16'18" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 172.48 }{ 30.5 } = 5.66 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 17 }{ 2 * sin 45° 27'25" } = 11.93 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 22**2+2 * 22**2 - 17**2 } }{ 2 } = 20.292 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 22**2+2 * 17**2 - 22**2 } }{ 2 } = 16.294 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 22**2+2 * 17**2 - 22**2 } }{ 2 } = 16.294 ; ;
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