7 19 19 triangle

Acute isosceles triangle.

Sides: a = 7   b = 19   c = 19

Area: T = 65.36219728894
Perimeter: p = 45
Semiperimeter: s = 22.5

Angle ∠ A = α = 21.23302157014° = 21°13'49″ = 0.37105371649 rad
Angle ∠ B = β = 79.38548921493° = 79°23'6″ = 1.38655277443 rad
Angle ∠ C = γ = 79.38548921493° = 79°23'6″ = 1.38655277443 rad

Height: ha = 18.6754849397
Height: hb = 6.88802076726
Height: hc = 6.88802076726

Median: ma = 18.6754849397
Median: mb = 10.71221426428
Median: mc = 10.71221426428

Inradius: r = 2.90549765729
Circumradius: R = 9.66554059245

Vertex coordinates: A[19; 0] B[0; 0] C[1.28994736842; 6.88802076726]
Centroid: CG[6.76331578947; 2.29334025575]
Coordinates of the circumscribed circle: U[9.5; 1.78804695124]
Coordinates of the inscribed circle: I[3.5; 2.90549765729]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.7769784299° = 158°46'11″ = 0.37105371649 rad
∠ B' = β' = 100.6155107851° = 100°36'54″ = 1.38655277443 rad
∠ C' = γ' = 100.6155107851° = 100°36'54″ = 1.38655277443 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 = 7 ; ; b = 19 ; ; c = 19 ; ;

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

p = a+b+c = 7+19+19 = 45 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 45 }{ 2 } = 22.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22.5 * (22.5-7)(22.5-19)(22.5-19) } ; ; T = sqrt{ 4272.19 } = 65.36 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 65.36 }{ 7 } = 18.67 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 65.36 }{ 19 } = 6.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 65.36 }{ 19 } = 6.88 ; ;

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{ 7**2-19**2-19**2 }{ 2 * 19 * 19 } ) = 21° 13'49" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-7**2-19**2 }{ 2 * 7 * 19 } ) = 79° 23'6" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-7**2-19**2 }{ 2 * 19 * 7 } ) = 79° 23'6" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 65.36 }{ 22.5 } = 2.9 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 21° 13'49" } = 9.67 ; ;




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