19 28 28 triangle

Acute isosceles triangle.

Sides: a = 19   b = 28   c = 28

Area: T = 250.222177663
Perimeter: p = 75
Semiperimeter: s = 37.5

Angle ∠ A = α = 39.66767238177° = 39°40' = 0.69223149341 rad
Angle ∠ B = β = 70.16766380911° = 70°10' = 1.22546388597 rad
Angle ∠ C = γ = 70.16766380911° = 70°10' = 1.22546388597 rad

Height: ha = 26.33991343821
Height: hb = 17.8732984045
Height: hc = 17.8732984045

Median: ma = 26.33991343821
Median: mb = 19.40436079119
Median: mc = 19.40436079119

Inradius: r = 6.67325807101
Circumradius: R = 14.88327973734

Vertex coordinates: A[28; 0] B[0; 0] C[6.44664285714; 17.8732984045]
Centroid: CG[11.48221428571; 5.95876613483]
Coordinates of the circumscribed circle: U[14; 5.05495205374]
Coordinates of the inscribed circle: I[9.5; 6.67325807101]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.3333276182° = 140°20' = 0.69223149341 rad
∠ B' = β' = 109.8333361909° = 109°50' = 1.22546388597 rad
∠ C' = γ' = 109.8333361909° = 109°50' = 1.22546388597 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 = 19 ; ; b = 28 ; ; c = 28 ; ;

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

p = a+b+c = 19+28+28 = 75 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 75 }{ 2 } = 37.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37.5 * (37.5-19)(37.5-28)(37.5-28) } ; ; T = sqrt{ 62610.94 } = 250.22 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 250.22 }{ 19 } = 26.34 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 250.22 }{ 28 } = 17.87 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 250.22 }{ 28 } = 17.87 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 28**2+28**2-19**2 }{ 2 * 28 * 28 } ) = 39° 40' ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 19**2+28**2-28**2 }{ 2 * 19 * 28 } ) = 70° 10' ; ; gamma = 180° - alpha - beta = 180° - 39° 40' - 70° 10' = 70° 10' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 250.22 }{ 37.5 } = 6.67 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 19 }{ 2 * sin 39° 40' } = 14.88 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 28**2 - 19**2 } }{ 2 } = 26.339 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 19**2 - 28**2 } }{ 2 } = 19.404 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 19**2 - 28**2 } }{ 2 } = 19.404 ; ;
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