16 16 21 triangle

Acute isosceles triangle.

Sides: a = 16   b = 16   c = 21

Area: T = 126.763331291
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 48.98655003343° = 48°59'8″ = 0.85549582666 rad
Angle ∠ B = β = 48.98655003343° = 48°59'8″ = 0.85549582666 rad
Angle ∠ C = γ = 82.02989993315° = 82°1'44″ = 1.43216761205 rad

Height: ha = 15.84554141138
Height: hb = 15.84554141138
Height: hc = 12.07326964676

Median: ma = 16.86771277934
Median: mb = 16.86771277934
Median: mc = 12.07326964676

Inradius: r = 4.78435212419
Circumradius: R = 10.6022436692

Vertex coordinates: A[21; 0] B[0; 0] C[10.5; 12.07326964676]
Centroid: CG[10.5; 4.02442321559]
Coordinates of the circumscribed circle: U[10.5; 1.47702597756]
Coordinates of the inscribed circle: I[10.5; 4.78435212419]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131.0144499666° = 131°52″ = 0.85549582666 rad
∠ B' = β' = 131.0144499666° = 131°52″ = 0.85549582666 rad
∠ C' = γ' = 97.97110006685° = 97°58'16″ = 1.43216761205 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 = 16 ; ; b = 16 ; ; c = 21 ; ;

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

p = a+b+c = 16+16+21 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-16)(26.5-16)(26.5-21) } ; ; T = sqrt{ 16068.94 } = 126.76 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 126.76 }{ 16 } = 15.85 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 126.76 }{ 16 } = 15.85 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 126.76 }{ 21 } = 12.07 ; ;

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{ 16**2-16**2-21**2 }{ 2 * 16 * 21 } ) = 48° 59'8" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-16**2-21**2 }{ 2 * 16 * 21 } ) = 48° 59'8" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 21**2-16**2-16**2 }{ 2 * 16 * 16 } ) = 82° 1'44" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 126.76 }{ 26.5 } = 4.78 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 48° 59'8" } = 10.6 ; ;




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