17 17 21 triangle

Acute isosceles triangle.

Sides: a = 17   b = 17   c = 21

Area: T = 140.382229055
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 51.85554868988° = 51°51'20″ = 0.90550489816 rad
Angle ∠ B = β = 51.85554868988° = 51°51'20″ = 0.90550489816 rad
Angle ∠ C = γ = 76.28990262025° = 76°17'21″ = 1.33114946904 rad

Height: ha = 16.51655635941
Height: hb = 16.51655635941
Height: hc = 13.37697419571

Median: ma = 17.11099386323
Median: mb = 17.11099386323
Median: mc = 13.37697419571

Inradius: r = 5.10548105654
Circumradius: R = 10.80879872045

Vertex coordinates: A[21; 0] B[0; 0] C[10.5; 13.37697419571]
Centroid: CG[10.5; 4.45765806524]
Coordinates of the circumscribed circle: U[10.5; 2.56217547526]
Coordinates of the inscribed circle: I[10.5; 5.10548105654]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.1454513101° = 128°8'40″ = 0.90550489816 rad
∠ B' = β' = 128.1454513101° = 128°8'40″ = 0.90550489816 rad
∠ C' = γ' = 103.7110973798° = 103°42'39″ = 1.33114946904 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 = 17 ; ; c = 21 ; ;

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

p = a+b+c = 17+17+21 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-17)(27.5-17)(27.5-21) } ; ; T = sqrt{ 19707.19 } = 140.38 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 140.38 }{ 17 } = 16.52 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 140.38 }{ 17 } = 16.52 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 140.38 }{ 21 } = 13.37 ; ;

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{ 17**2-17**2-21**2 }{ 2 * 17 * 21 } ) = 51° 51'20" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-17**2-21**2 }{ 2 * 17 * 21 } ) = 51° 51'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 21**2-17**2-17**2 }{ 2 * 17 * 17 } ) = 76° 17'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 140.38 }{ 27.5 } = 5.1 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 51° 51'20" } = 10.81 ; ;




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