8 9 11 triangle

Acute scalene triangle.

Sides: a = 8   b = 9   c = 11

Area: T = 35.49664786986
Perimeter: p = 28
Semiperimeter: s = 14

Angle ∠ A = α = 45.81656148467° = 45°48'56″ = 0.87996333279 rad
Angle ∠ B = β = 53.77884533802° = 53°46'42″ = 0.93986110781 rad
Angle ∠ C = γ = 80.40659317731° = 80°24'21″ = 1.40333482476 rad

Height: ha = 8.87441196746
Height: hb = 7.88881063775
Height: hc = 6.45439052179

Median: ma = 9.22195444573
Median: mb = 8.5
Median: mc = 6.5

Inradius: r = 2.53554627642
Circumradius: R = 5.57880180812

Vertex coordinates: A[11; 0] B[0; 0] C[4.72772727273; 6.45439052179]
Centroid: CG[5.24224242424; 2.15113017393]
Coordinates of the circumscribed circle: U[5.5; 0.93296696802]
Coordinates of the inscribed circle: I[5; 2.53554627642]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.1844385153° = 134°11'4″ = 0.87996333279 rad
∠ B' = β' = 126.222154662° = 126°13'18″ = 0.93986110781 rad
∠ C' = γ' = 99.59440682269° = 99°35'39″ = 1.40333482476 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 = 8 ; ; b = 9 ; ; c = 11 ; ;

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

p = a+b+c = 8+9+11 = 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 * (14-8)(14-9)(14-11) } ; ; T = sqrt{ 1260 } = 35.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 35.5 }{ 8 } = 8.87 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 35.5 }{ 9 } = 7.89 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 35.5 }{ 11 } = 6.45 ; ;

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{ 8**2-9**2-11**2 }{ 2 * 9 * 11 } ) = 45° 48'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 9**2-8**2-11**2 }{ 2 * 8 * 11 } ) = 53° 46'42" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 11**2-8**2-9**2 }{ 2 * 9 * 8 } ) = 80° 24'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 35.5 }{ 14 } = 2.54 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 45° 48'56" } = 5.58 ; ;




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

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