18 28 28 triangle

Acute isosceles triangle.

Sides: a = 18   b = 28   c = 28

Area: T = 238.6277324504
Perimeter: p = 74
Semiperimeter: s = 37

Angle ∠ A = α = 37.4998681694° = 37°29'55″ = 0.65444754607 rad
Angle ∠ B = β = 71.2510659153° = 71°15'2″ = 1.24435585964 rad
Angle ∠ C = γ = 71.2510659153° = 71°15'2″ = 1.24435585964 rad

Height: ha = 26.51441471671
Height: hb = 17.04548088932
Height: hc = 17.04548088932

Median: ma = 26.51441471671
Median: mb = 18.92108879284
Median: mc = 18.92108879284

Inradius: r = 6.44993871488
Circumradius: R = 14.78545600135

Vertex coordinates: A[28; 0] B[0; 0] C[5.78657142857; 17.04548088932]
Centroid: CG[11.26219047619; 5.68216029644]
Coordinates of the circumscribed circle: U[14; 4.75221800043]
Coordinates of the inscribed circle: I[9; 6.44993871488]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.5011318306° = 142°30'5″ = 0.65444754607 rad
∠ B' = β' = 108.7499340847° = 108°44'58″ = 1.24435585964 rad
∠ C' = γ' = 108.7499340847° = 108°44'58″ = 1.24435585964 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 = 18 ; ; b = 28 ; ; c = 28 ; ;

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

p = a+b+c = 18+28+28 = 74 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 74 }{ 2 } = 37 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37 * (37-18)(37-28)(37-28) } ; ; T = sqrt{ 56943 } = 238.63 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 238.63 }{ 18 } = 26.51 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 238.63 }{ 28 } = 17.04 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 238.63 }{ 28 } = 17.04 ; ;

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**2-18**2 }{ 2 * 28 * 28 } ) = 37° 29'55" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 18**2+28**2-28**2 }{ 2 * 18 * 28 } ) = 71° 15'2" ; ; gamma = 180° - alpha - beta = 180° - 37° 29'55" - 71° 15'2" = 71° 15'2" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 238.63 }{ 37 } = 6.45 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 18 }{ 2 * sin 37° 29'55" } = 14.78 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 28**2 - 18**2 } }{ 2 } = 26.514 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 18**2 - 28**2 } }{ 2 } = 18.921 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 18**2 - 28**2 } }{ 2 } = 18.921 ; ;
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