5 14 14 triangle

Acute isosceles triangle.

Sides: a = 5   b = 14   c = 14

Area: T = 34.43774432849
Perimeter: p = 33
Semiperimeter: s = 16.5

Angle ∠ A = α = 20.57331212229° = 20°34'23″ = 0.35990687028 rad
Angle ∠ B = β = 79.71334393885° = 79°42'48″ = 1.39112619754 rad
Angle ∠ C = γ = 79.71334393885° = 79°42'48″ = 1.39112619754 rad

Height: ha = 13.7754977314
Height: hb = 4.9219634755
Height: hc = 4.9219634755

Median: ma = 13.7754977314
Median: mb = 7.84221935707
Median: mc = 7.84221935707

Inradius: r = 2.08771177748
Circumradius: R = 7.11443492847

Vertex coordinates: A[14; 0] B[0; 0] C[0.89328571429; 4.9219634755]
Centroid: CG[4.96442857143; 1.64398782517]
Coordinates of the circumscribed circle: U[7; 1.27704195151]
Coordinates of the inscribed circle: I[2.5; 2.08771177748]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.4276878777° = 159°25'37″ = 0.35990687028 rad
∠ B' = β' = 100.2876560611° = 100°17'12″ = 1.39112619754 rad
∠ C' = γ' = 100.2876560611° = 100°17'12″ = 1.39112619754 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 = 14 ; ; c = 14 ; ;

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

p = a+b+c = 5+14+14 = 33 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 33 }{ 2 } = 16.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16.5 * (16.5-5)(16.5-14)(16.5-14) } ; ; T = sqrt{ 1185.94 } = 34.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 34.44 }{ 5 } = 13.77 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 34.44 }{ 14 } = 4.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 34.44 }{ 14 } = 4.92 ; ;

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**2-14**2-14**2 }{ 2 * 14 * 14 } ) = 20° 34'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-5**2-14**2 }{ 2 * 5 * 14 } ) = 79° 42'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14**2-5**2-14**2 }{ 2 * 14 * 5 } ) = 79° 42'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 34.44 }{ 16.5 } = 2.09 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 20° 34'23" } = 7.11 ; ;




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