6 16 16 triangle

Acute isosceles triangle.

Sides: a = 6   b = 16   c = 16

Area: T = 47.14987009365
Perimeter: p = 38
Semiperimeter: s = 19

Angle ∠ A = α = 21.61438457497° = 21°36'50″ = 0.37772327724 rad
Angle ∠ B = β = 79.19330771251° = 79°11'35″ = 1.38221799406 rad
Angle ∠ C = γ = 79.19330771251° = 79°11'35″ = 1.38221799406 rad

Height: ha = 15.71662336455
Height: hb = 5.89435876171
Height: hc = 5.89435876171

Median: ma = 15.71662336455
Median: mb = 9.05553851381
Median: mc = 9.05553851381

Inradius: r = 2.48215105756
Circumradius: R = 8.14444449661

Vertex coordinates: A[16; 0] B[0; 0] C[1.125; 5.89435876171]
Centroid: CG[5.70883333333; 1.96545292057]
Coordinates of the circumscribed circle: U[8; 1.52770834311]
Coordinates of the inscribed circle: I[3; 2.48215105756]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.386615425° = 158°23'10″ = 0.37772327724 rad
∠ B' = β' = 100.8076922875° = 100°48'25″ = 1.38221799406 rad
∠ C' = γ' = 100.8076922875° = 100°48'25″ = 1.38221799406 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 = 6 ; ; b = 16 ; ; c = 16 ; ;

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

p = a+b+c = 6+16+16 = 38 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 38 }{ 2 } = 19 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19 * (19-6)(19-16)(19-16) } ; ; T = sqrt{ 2223 } = 47.15 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 47.15 }{ 6 } = 15.72 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 47.15 }{ 16 } = 5.89 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 47.15 }{ 16 } = 5.89 ; ;

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{ 6**2-16**2-16**2 }{ 2 * 16 * 16 } ) = 21° 36'50" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-6**2-16**2 }{ 2 * 6 * 16 } ) = 79° 11'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-6**2-16**2 }{ 2 * 16 * 6 } ) = 79° 11'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 47.15 }{ 19 } = 2.48 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 21° 36'50" } = 8.14 ; ;




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