4 11 13 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 11   c = 13

Area: T = 20.49439015319
Perimeter: p = 28
Semiperimeter: s = 14

Angle ∠ A = α = 16.65661861814° = 16°39'22″ = 0.29107052897 rad
Angle ∠ B = β = 52.02201275551° = 52°1'12″ = 0.90879225031 rad
Angle ∠ C = γ = 111.3243686263° = 111°19'25″ = 1.94329648608 rad

Height: ha = 10.2476950766
Height: hb = 3.72661639149
Height: hc = 3.1532907928

Median: ma = 11.8744342087
Median: mb = 7.8989866919
Median: mc = 5.1233475383

Inradius: r = 1.46438501094
Circumradius: R = 6.97876855216

Vertex coordinates: A[13; 0] B[0; 0] C[2.46215384615; 3.1532907928]
Centroid: CG[5.15438461538; 1.05109693093]
Coordinates of the circumscribed circle: U[6.5; -2.53773401897]
Coordinates of the inscribed circle: I[3; 1.46438501094]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.3443813819° = 163°20'38″ = 0.29107052897 rad
∠ B' = β' = 127.9879872445° = 127°58'48″ = 0.90879225031 rad
∠ C' = γ' = 68.67663137365° = 68°40'35″ = 1.94329648608 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 = 4 ; ; b = 11 ; ; c = 13 ; ;

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

p = a+b+c = 4+11+13 = 28 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 28 }{ 2 } = 14 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 14 * (14-4)(14-11)(14-13) } ; ; T = sqrt{ 420 } = 20.49 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 20.49 }{ 4 } = 10.25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 20.49 }{ 11 } = 3.73 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 20.49 }{ 13 } = 3.15 ; ;

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{ 4**2-11**2-13**2 }{ 2 * 11 * 13 } ) = 16° 39'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-4**2-13**2 }{ 2 * 4 * 13 } ) = 52° 1'12" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 13**2-4**2-11**2 }{ 2 * 11 * 4 } ) = 111° 19'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 20.49 }{ 14 } = 1.46 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 16° 39'22" } = 6.98 ; ;




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