5 30 30 triangle

Acute isosceles triangle.

Sides: a = 5   b = 30   c = 30

Area: T = 74.73991296444
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 9.56603836944° = 9°33'37″ = 0.16768601732 rad
Angle ∠ B = β = 85.22198081528° = 85°13'11″ = 1.48773662402 rad
Angle ∠ C = γ = 85.22198081528° = 85°13'11″ = 1.48773662402 rad

Height: ha = 29.89656518578
Height: hb = 4.9832608643
Height: hc = 4.9832608643

Median: ma = 29.89656518578
Median: mb = 15.41110350074
Median: mc = 15.41110350074

Inradius: r = 2.32996655275
Circumradius: R = 15.05223561801

Vertex coordinates: A[30; 0] B[0; 0] C[0.41766666667; 4.9832608643]
Centroid: CG[10.13988888889; 1.66108695477]
Coordinates of the circumscribed circle: U[15; 1.2544363015]
Coordinates of the inscribed circle: I[2.5; 2.32996655275]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.4439616306° = 170°26'23″ = 0.16768601732 rad
∠ B' = β' = 94.78801918472° = 94°46'49″ = 1.48773662402 rad
∠ C' = γ' = 94.78801918472° = 94°46'49″ = 1.48773662402 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 = 5 ; ; b = 30 ; ; c = 30 ; ;

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

p = a+b+c = 5+30+30 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-5)(32.5-30)(32.5-30) } ; ; T = sqrt{ 5585.94 } = 74.74 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 74.74 }{ 5 } = 29.9 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 74.74 }{ 30 } = 4.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 74.74 }{ 30 } = 4.98 ; ;

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{ 5**2-30**2-30**2 }{ 2 * 30 * 30 } ) = 9° 33'37" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 30**2-5**2-30**2 }{ 2 * 5 * 30 } ) = 85° 13'11" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-5**2-30**2 }{ 2 * 30 * 5 } ) = 85° 13'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 74.74 }{ 32.5 } = 2.3 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 9° 33'37" } = 15.05 ; ;




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