8 30 30 triangle

Acute isosceles triangle.

Sides: a = 8   b = 30   c = 30

Area: T = 118.9298549979
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 15.32545113215° = 15°19'28″ = 0.26774631788 rad
Angle ∠ B = β = 82.33877443392° = 82°20'16″ = 1.43770647374 rad
Angle ∠ C = γ = 82.33877443392° = 82°20'16″ = 1.43770647374 rad

Height: ha = 29.73221374946
Height: hb = 7.92985699986
Height: hc = 7.92985699986

Median: ma = 29.73221374946
Median: mb = 16.03112195419
Median: mc = 16.03112195419

Inradius: r = 3.49878985288
Circumradius: R = 15.13551378649

Vertex coordinates: A[30; 0] B[0; 0] C[1.06766666667; 7.92985699986]
Centroid: CG[10.35655555556; 2.64328566662]
Coordinates of the circumscribed circle: U[15; 2.0188018382]
Coordinates of the inscribed circle: I[4; 3.49878985288]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.6755488678° = 164°40'32″ = 0.26774631788 rad
∠ B' = β' = 97.66222556608° = 97°39'44″ = 1.43770647374 rad
∠ C' = γ' = 97.66222556608° = 97°39'44″ = 1.43770647374 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 = 8 ; ; b = 30 ; ; c = 30 ; ;

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

p = a+b+c = 8+30+30 = 68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 68 }{ 2 } = 34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34 * (34-8)(34-30)(34-30) } ; ; T = sqrt{ 14144 } = 118.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 118.93 }{ 8 } = 29.73 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 118.93 }{ 30 } = 7.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 118.93 }{ 30 } = 7.93 ; ;

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{ 8**2-30**2-30**2 }{ 2 * 30 * 30 } ) = 15° 19'28" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 30**2-8**2-30**2 }{ 2 * 8 * 30 } ) = 82° 20'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-8**2-30**2 }{ 2 * 30 * 8 } ) = 82° 20'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 118.93 }{ 34 } = 3.5 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 15° 19'28" } = 15.14 ; ;




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