10 28 28 triangle

Acute isosceles triangle.

Sides: a = 10   b = 28   c = 28

Area: T = 137.754977314
Perimeter: p = 66
Semiperimeter: s = 33

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 = 27.55499546279
Height: hb = 9.839926951
Height: hc = 9.839926951

Median: ma = 27.55499546279
Median: mb = 15.68443871414
Median: mc = 15.68443871414

Inradius: r = 4.17442355497
Circumradius: R = 14.22986985694

Vertex coordinates: A[28; 0] B[0; 0] C[1.78657142857; 9.839926951]
Centroid: CG[9.92985714286; 3.28797565033]
Coordinates of the circumscribed circle: U[14; 2.54108390302]
Coordinates of the inscribed circle: I[5; 4.17442355497]

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 = 10 ; ; b = 28 ; ; c = 28 ; ;

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

p = a+b+c = 10+28+28 = 66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 66 }{ 2 } = 33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33 * (33-10)(33-28)(33-28) } ; ; T = sqrt{ 18975 } = 137.75 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 137.75 }{ 10 } = 27.55 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 137.75 }{ 28 } = 9.84 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 137.75 }{ 28 } = 9.84 ; ;

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{ 10**2-28**2-28**2 }{ 2 * 28 * 28 } ) = 20° 34'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-10**2-28**2 }{ 2 * 10 * 28 } ) = 79° 42'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-10**2-28**2 }{ 2 * 28 * 10 } ) = 79° 42'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 137.75 }{ 33 } = 4.17 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 20° 34'23" } = 14.23 ; ;




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