12.8 11.4 3.3 triangle

Obtuse scalene triangle.

Sides: a = 12.8   b = 11.4   c = 3.3

Area: T = 17.91103976435
Perimeter: p = 27.5
Semiperimeter: s = 13.75

Angle ∠ A = α = 107.7921590573° = 107°47'30″ = 1.88113181615 rad
Angle ∠ B = β = 57.99880641654° = 57°59'53″ = 1.01222571795 rad
Angle ∠ C = γ = 14.21103452616° = 14°12'37″ = 0.24880173127 rad

Height: ha = 2.79884996318
Height: hb = 3.14221750252
Height: hc = 10.85547864506

Median: ma = 5.42881672782
Median: mb = 7.4087766195
Median: mc = 12.00773935556

Inradius: r = 1.30325743741
Circumradius: R = 6.72114588082

Vertex coordinates: A[3.3; 0] B[0; 0] C[6.78333333333; 10.85547864506]
Centroid: CG[3.36111111111; 3.61882621502]
Coordinates of the circumscribed circle: U[1.65; 6.51657891702]
Coordinates of the inscribed circle: I[2.35; 1.30325743741]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 72.2088409427° = 72°12'30″ = 1.88113181615 rad
∠ B' = β' = 122.0021935835° = 122°7″ = 1.01222571795 rad
∠ C' = γ' = 165.7989654738° = 165°47'23″ = 0.24880173127 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 = 12.8 ; ; b = 11.4 ; ; c = 3.3 ; ;

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

p = a+b+c = 12.8+11.4+3.3 = 27.5 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 27.5 }{ 2 } = 13.75 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13.75 * (13.75-12.8)(13.75-11.4)(13.75-3.3) } ; ; T = sqrt{ 320.78 } = 17.91 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 17.91 }{ 12.8 } = 2.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 17.91 }{ 11.4 } = 3.14 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 17.91 }{ 3.3 } = 10.85 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 11.4**2+3.3**2-12.8**2 }{ 2 * 11.4 * 3.3 } ) = 107° 47'30" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 12.8**2+3.3**2-11.4**2 }{ 2 * 12.8 * 3.3 } ) = 57° 59'53" ; ;
 gamma = 180° - alpha - beta = 180° - 107° 47'30" - 57° 59'53" = 14° 12'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 17.91 }{ 13.75 } = 1.3 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 12.8 }{ 2 * sin 107° 47'30" } = 6.72 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 11.4**2+2 * 3.3**2 - 12.8**2 } }{ 2 } = 5.428 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.3**2+2 * 12.8**2 - 11.4**2 } }{ 2 } = 7.408 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 11.4**2+2 * 12.8**2 - 3.3**2 } }{ 2 } = 12.007 ; ;
Calculate another triangle


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

See more information about triangles or more details on solving triangles.