1 21 21 triangle

Acute isosceles triangle.

Sides: a = 1   b = 21   c = 21

Area: T = 10.49770233876
Perimeter: p = 43
Semiperimeter: s = 21.5

Angle ∠ A = α = 2.72986283013° = 2°43'43″ = 0.04876235479 rad
Angle ∠ B = β = 88.63656858493° = 88°38'8″ = 1.54769845528 rad
Angle ∠ C = γ = 88.63656858493° = 88°38'8″ = 1.54769845528 rad

Height: ha = 20.99440467752
Height: hb = 10.9997165131
Height: hc = 10.9997165131

Median: ma = 20.99440467752
Median: mb = 10.52437825899
Median: mc = 10.52437825899

Inradius: r = 0.48882336459
Circumradius: R = 10.50329774565

Vertex coordinates: A[21; 0] B[0; 0] C[0.02438095238; 10.9997165131]
Centroid: CG[7.00879365079; 0.33332388377]
Coordinates of the circumscribed circle: U[10.5; 0.25500708918]
Coordinates of the inscribed circle: I[0.5; 0.48882336459]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 177.2711371699° = 177°16'17″ = 0.04876235479 rad
∠ B' = β' = 91.36443141507° = 91°21'52″ = 1.54769845528 rad
∠ C' = γ' = 91.36443141507° = 91°21'52″ = 1.54769845528 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 = 1 ; ; b = 21 ; ; c = 21 ; ;

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

p = a+b+c = 1+21+21 = 43 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 43 }{ 2 } = 21.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21.5 * (21.5-1)(21.5-21)(21.5-21) } ; ; T = sqrt{ 110.19 } = 10.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 10.5 }{ 1 } = 20.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 10.5 }{ 21 } = 1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 10.5 }{ 21 } = 1 ; ;

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{ 1**2-21**2-21**2 }{ 2 * 21 * 21 } ) = 2° 43'43" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-1**2-21**2 }{ 2 * 1 * 21 } ) = 88° 38'8" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 21**2-1**2-21**2 }{ 2 * 21 * 1 } ) = 88° 38'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 10.5 }{ 21.5 } = 0.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1 }{ 2 * sin 2° 43'43" } = 10.5 ; ;




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