2 19 19 triangle

Acute isosceles triangle.

Sides: a = 2   b = 19   c = 19

Area: T = 18.9743665961
Perimeter: p = 40
Semiperimeter: s = 20

Angle ∠ A = α = 6.03439226196° = 6°2'2″ = 0.10553118165 rad
Angle ∠ B = β = 86.98330386902° = 86°58'59″ = 1.51881404185 rad
Angle ∠ C = γ = 86.98330386902° = 86°58'59″ = 1.51881404185 rad

Height: ha = 18.9743665961
Height: hb = 1.99772279959
Height: hc = 1.99772279959

Median: ma = 18.9743665961
Median: mb = 9.60546863561
Median: mc = 9.60546863561

Inradius: r = 0.94986832981
Circumradius: R = 9.51331852943

Vertex coordinates: A[19; 0] B[0; 0] C[0.10552631579; 1.99772279959]
Centroid: CG[6.36884210526; 0.66657426653]
Coordinates of the circumscribed circle: U[9.5; 0.50106939629]
Coordinates of the inscribed circle: I[1; 0.94986832981]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 173.966607738° = 173°57'58″ = 0.10553118165 rad
∠ B' = β' = 93.01769613098° = 93°1'1″ = 1.51881404185 rad
∠ C' = γ' = 93.01769613098° = 93°1'1″ = 1.51881404185 rad

Calculate another triangle




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 = 2 ; ; b = 19 ; ; c = 19 ; ;

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

p = a+b+c = 2+19+19 = 40 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 40 }{ 2 } = 20 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20 * (20-2)(20-19)(20-19) } ; ; T = sqrt{ 360 } = 18.97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 18.97 }{ 2 } = 18.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 18.97 }{ 19 } = 2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 18.97 }{ 19 } = 2 ; ;

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{ 2**2-19**2-19**2 }{ 2 * 19 * 19 } ) = 6° 2'2" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-2**2-19**2 }{ 2 * 2 * 19 } ) = 86° 58'59" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-2**2-19**2 }{ 2 * 19 * 2 } ) = 86° 58'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 18.97 }{ 20 } = 0.95 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 6° 2'2" } = 9.51 ; ;




Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.