10 21 21 triangle

Acute isosceles triangle.

Sides: a = 10   b = 21   c = 21

Area: T = 101.9880390272
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 27.54882939961° = 27°32'54″ = 0.48108084335 rad
Angle ∠ B = β = 76.2265853002° = 76°13'33″ = 1.333039211 rad
Angle ∠ C = γ = 76.2265853002° = 76°13'33″ = 1.333039211 rad

Height: ha = 20.39660780544
Height: hb = 9.71224181211
Height: hc = 9.71224181211

Median: ma = 20.39660780544
Median: mb = 12.65989889012
Median: mc = 12.65989889012

Inradius: r = 3.92223227028
Circumradius: R = 10.81109019495

Vertex coordinates: A[21; 0] B[0; 0] C[2.3810952381; 9.71224181211]
Centroid: CG[7.79436507937; 3.2377472707]
Coordinates of the circumscribed circle: U[10.5; 2.57440242737]
Coordinates of the inscribed circle: I[5; 3.92223227028]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.4521706004° = 152°27'6″ = 0.48108084335 rad
∠ B' = β' = 103.7744146998° = 103°46'27″ = 1.333039211 rad
∠ C' = γ' = 103.7744146998° = 103°46'27″ = 1.333039211 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 = 10 ; ; b = 21 ; ; c = 21 ; ;

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

p = a+b+c = 10+21+21 = 52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 52 }{ 2 } = 26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26 * (26-10)(26-21)(26-21) } ; ; T = sqrt{ 10400 } = 101.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 101.98 }{ 10 } = 20.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 101.98 }{ 21 } = 9.71 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 101.98 }{ 21 } = 9.71 ; ;

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{ 10**2-21**2-21**2 }{ 2 * 21 * 21 } ) = 27° 32'54" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-10**2-21**2 }{ 2 * 10 * 21 } ) = 76° 13'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 21**2-10**2-21**2 }{ 2 * 21 * 10 } ) = 76° 13'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 101.98 }{ 26 } = 3.92 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 27° 32'54" } = 10.81 ; ;




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