6 11 15 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 11   c = 15

Area: T = 28.28442712475
Perimeter: p = 32
Semiperimeter: s = 16

Angle ∠ A = α = 20.05499757242° = 20°3' = 0.35499380913 rad
Angle ∠ B = β = 38.9422441269° = 38°56'33″ = 0.68796738189 rad
Angle ∠ C = γ = 121.0087583007° = 121°27″ = 2.11219807434 rad

Height: ha = 9.42880904158
Height: hb = 5.14325947723
Height: hc = 3.77112361663

Median: ma = 12.80662484749
Median: mb = 10.01224921973
Median: mc = 4.7176990566

Inradius: r = 1.7687766953
Circumradius: R = 8.75504464172

Vertex coordinates: A[15; 0] B[0; 0] C[4.66766666667; 3.77112361663]
Centroid: CG[6.55655555556; 1.25770787221]
Coordinates of the circumscribed circle: U[7.5; -4.50878057301]
Coordinates of the inscribed circle: I[5; 1.7687766953]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.9550024276° = 159°57' = 0.35499380913 rad
∠ B' = β' = 141.0587558731° = 141°3'27″ = 0.68796738189 rad
∠ C' = γ' = 58.99224169931° = 58°59'33″ = 2.11219807434 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 = 6 ; ; b = 11 ; ; c = 15 ; ;

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

p = a+b+c = 6+11+15 = 32 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 32 }{ 2 } = 16 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16 * (16-6)(16-11)(16-15) } ; ; T = sqrt{ 800 } = 28.28 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 28.28 }{ 6 } = 9.43 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 28.28 }{ 11 } = 5.14 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 28.28 }{ 15 } = 3.77 ; ;

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{ 6**2-11**2-15**2 }{ 2 * 11 * 15 } ) = 20° 3' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-6**2-15**2 }{ 2 * 6 * 15 } ) = 38° 56'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 15**2-6**2-11**2 }{ 2 * 11 * 6 } ) = 121° 27" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 28.28 }{ 16 } = 1.77 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 20° 3' } = 8.75 ; ;




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

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