102 102 90 triangle

Acute isosceles triangle.

Sides: a = 102   b = 102   c = 90

Area: T = 4119.165950165
Perimeter: p = 294
Semiperimeter: s = 147

Angle ∠ A = α = 63.8211031296° = 63°49'16″ = 1.11438871281 rad
Angle ∠ B = β = 63.8211031296° = 63°49'16″ = 1.11438871281 rad
Angle ∠ C = γ = 52.3587937408° = 52°21'29″ = 0.91438183973 rad

Height: ha = 80.76878333656
Height: hb = 80.76878333656
Height: hc = 91.53768778144

Median: ma = 81.55436633144
Median: mb = 81.55436633144
Median: mc = 91.53768778144

Inradius: r = 28.02114932085
Circumradius: R = 56.83295546474

Vertex coordinates: A[90; 0] B[0; 0] C[45; 91.53768778144]
Centroid: CG[45; 30.51222926048]
Coordinates of the circumscribed circle: U[45; 34.7077323167]
Coordinates of the inscribed circle: I[45; 28.02114932085]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 116.1798968704° = 116°10'44″ = 1.11438871281 rad
∠ B' = β' = 116.1798968704° = 116°10'44″ = 1.11438871281 rad
∠ C' = γ' = 127.6422062592° = 127°38'31″ = 0.91438183973 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 = 102 ; ; b = 102 ; ; c = 90 ; ;

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

p = a+b+c = 102+102+90 = 294 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 294 }{ 2 } = 147 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 147 * (147-102)(147-102)(147-90) } ; ; T = sqrt{ 16967475 } = 4119.16 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4119.16 }{ 102 } = 80.77 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4119.16 }{ 102 } = 80.77 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4119.16 }{ 90 } = 91.54 ; ;

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{ 102**2-102**2-90**2 }{ 2 * 102 * 90 } ) = 63° 49'16" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 102**2-102**2-90**2 }{ 2 * 102 * 90 } ) = 63° 49'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 90**2-102**2-102**2 }{ 2 * 102 * 102 } ) = 52° 21'29" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4119.16 }{ 147 } = 28.02 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 102 }{ 2 * sin 63° 49'16" } = 56.83 ; ;




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