19 27 27 triangle

Acute isosceles triangle.

Sides: a = 19   b = 27   c = 27

Area: T = 240.0988287166
Perimeter: p = 73
Semiperimeter: s = 36.5

Angle ∠ A = α = 41.20112490993° = 41°12'5″ = 0.71990974527 rad
Angle ∠ B = β = 69.39993754503° = 69°23'58″ = 1.21112476004 rad
Angle ∠ C = γ = 69.39993754503° = 69°23'58″ = 1.21112476004 rad

Height: ha = 25.27435039122
Height: hb = 17.78550583086
Height: hc = 17.78550583086

Median: ma = 25.27435039122
Median: mb = 19.04659969547
Median: mc = 19.04659969547

Inradius: r = 6.57880352648
Circumradius: R = 14.42222186708

Vertex coordinates: A[27; 0] B[0; 0] C[6.68551851852; 17.78550583086]
Centroid: CG[11.22883950617; 5.92883527695]
Coordinates of the circumscribed circle: U[13.5; 5.07444843471]
Coordinates of the inscribed circle: I[9.5; 6.57880352648]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.7998750901° = 138°47'56″ = 0.71990974527 rad
∠ B' = β' = 110.601062455° = 110°36'2″ = 1.21112476004 rad
∠ C' = γ' = 110.601062455° = 110°36'2″ = 1.21112476004 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 = 27 ; ; c = 27 ; ;

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

p = a+b+c = 19+27+27 = 73 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 73 }{ 2 } = 36.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36.5 * (36.5-19)(36.5-27)(36.5-27) } ; ; T = sqrt{ 57647.19 } = 240.1 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 240.1 }{ 19 } = 25.27 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 240.1 }{ 27 } = 17.79 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 240.1 }{ 27 } = 17.79 ; ;

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{ 19**2-27**2-27**2 }{ 2 * 27 * 27 } ) = 41° 12'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-19**2-27**2 }{ 2 * 19 * 27 } ) = 69° 23'58" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-19**2-27**2 }{ 2 * 27 * 19 } ) = 69° 23'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 240.1 }{ 36.5 } = 6.58 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 41° 12'5" } = 14.42 ; ;




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