9 11 16 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 11   c = 16

Area: T = 47.62435235992
Perimeter: p = 36
Semiperimeter: s = 18

Angle ∠ A = α = 32.76437577589° = 32°45'50″ = 0.57218354482 rad
Angle ∠ B = β = 41.41096221093° = 41°24'35″ = 0.72327342478 rad
Angle ∠ C = γ = 105.8276620132° = 105°49'36″ = 1.84770229576 rad

Height: ha = 10.58330052443
Height: hb = 8.65988224726
Height: hc = 5.95329404499

Median: ma = 12.97111217711
Median: mb = 11.75879760163
Median: mc = 6.08327625303

Inradius: r = 2.64657513111
Circumradius: R = 8.31552184062

Vertex coordinates: A[16; 0] B[0; 0] C[6.75; 5.95329404499]
Centroid: CG[7.58333333333; 1.98443134833]
Coordinates of the circumscribed circle: U[8; -2.26877868381]
Coordinates of the inscribed circle: I[7; 2.64657513111]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.2366242241° = 147°14'10″ = 0.57218354482 rad
∠ B' = β' = 138.5990377891° = 138°35'25″ = 0.72327342478 rad
∠ C' = γ' = 74.17333798681° = 74°10'24″ = 1.84770229576 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 = 9 ; ; b = 11 ; ; c = 16 ; ;

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

p = a+b+c = 9+11+16 = 36 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 36 }{ 2 } = 18 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18 * (18-9)(18-11)(18-16) } ; ; T = sqrt{ 2268 } = 47.62 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 47.62 }{ 9 } = 10.58 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 47.62 }{ 11 } = 8.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 47.62 }{ 16 } = 5.95 ; ;

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{ 9**2-11**2-16**2 }{ 2 * 11 * 16 } ) = 32° 45'50" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-9**2-16**2 }{ 2 * 9 * 16 } ) = 41° 24'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-9**2-11**2 }{ 2 * 11 * 9 } ) = 105° 49'36" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 47.62 }{ 18 } = 2.65 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 32° 45'50" } = 8.32 ; ;




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

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