3 10 11 triangle

Obtuse scalene triangle.

Sides: a = 3   b = 10   c = 11

Area: T = 14.69769384567
Perimeter: p = 24
Semiperimeter: s = 12

Angle ∠ A = α = 15.49987327566° = 15°29'55″ = 0.27105039165 rad
Angle ∠ B = β = 62.96443082106° = 62°57'52″ = 1.09989344895 rad
Angle ∠ C = γ = 101.5376959033° = 101°32'13″ = 1.77221542476 rad

Height: ha = 9.79879589711
Height: hb = 2.93993876913
Height: hc = 2.67221706285

Median: ma = 10.40443260233
Median: mb = 6.32545553203
Median: mc = 4.92444289009

Inradius: r = 1.22547448714
Circumradius: R = 5.61334139939

Vertex coordinates: A[11; 0] B[0; 0] C[1.36436363636; 2.67221706285]
Centroid: CG[4.12112121212; 0.89107235428]
Coordinates of the circumscribed circle: U[5.5; -1.12326827988]
Coordinates of the inscribed circle: I[2; 1.22547448714]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.5011267243° = 164°30'5″ = 0.27105039165 rad
∠ B' = β' = 117.0365691789° = 117°2'8″ = 1.09989344895 rad
∠ C' = γ' = 78.46330409672° = 78°27'47″ = 1.77221542476 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 = 3 ; ; b = 10 ; ; c = 11 ; ;

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

p = a+b+c = 3+10+11 = 24 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 24 }{ 2 } = 12 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12 * (12-3)(12-10)(12-11) } ; ; T = sqrt{ 216 } = 14.7 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 14.7 }{ 3 } = 9.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 14.7 }{ 10 } = 2.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 14.7 }{ 11 } = 2.67 ; ;

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{ 3**2-10**2-11**2 }{ 2 * 10 * 11 } ) = 15° 29'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 10**2-3**2-11**2 }{ 2 * 3 * 11 } ) = 62° 57'52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 11**2-3**2-10**2 }{ 2 * 10 * 3 } ) = 101° 32'13" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 14.7 }{ 12 } = 1.22 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 15° 29'55" } = 5.61 ; ;




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

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