3 8 8 triangle

Acute isosceles triangle.

Sides: a = 3   b = 8   c = 8

Area: T = 11.78771752341
Perimeter: p = 19
Semiperimeter: s = 9.5

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 = 7.85881168228
Height: hb = 2.94767938085
Height: hc = 2.94767938085

Median: ma = 7.85881168228
Median: mb = 4.52876925691
Median: mc = 4.52876925691

Inradius: r = 1.24107552878
Circumradius: R = 4.0722222483

Vertex coordinates: A[8; 0] B[0; 0] C[0.56325; 2.94767938085]
Centroid: CG[2.85441666667; 0.98222646028]
Coordinates of the circumscribed circle: U[4; 0.76435417156]
Coordinates of the inscribed circle: I[1.5; 1.24107552878]

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 = 3 ; ; b = 8 ; ; c = 8 ; ;

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

p = a+b+c = 3+8+8 = 19 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 19 }{ 2 } = 9.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 9.5 * (9.5-3)(9.5-8)(9.5-8) } ; ; T = sqrt{ 138.94 } = 11.79 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 11.79 }{ 3 } = 7.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 11.79 }{ 8 } = 2.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 11.79 }{ 8 } = 2.95 ; ;

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{ 3**2-8**2-8**2 }{ 2 * 8 * 8 } ) = 21° 36'50" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 8**2-3**2-8**2 }{ 2 * 3 * 8 } ) = 79° 11'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 8**2-3**2-8**2 }{ 2 * 8 * 3 } ) = 79° 11'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 11.79 }{ 9.5 } = 1.24 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 21° 36'50" } = 4.07 ; ;




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