4 10 11 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 10   c = 11

Area: T = 19.96108992783
Perimeter: p = 25
Semiperimeter: s = 12.5

Angle ∠ A = α = 21.28799664684° = 21°16'48″ = 0.37114054796 rad
Angle ∠ B = β = 65.13767118331° = 65°8'12″ = 1.13768500854 rad
Angle ∠ C = γ = 93.58333216985° = 93°35' = 1.63333370886 rad

Height: ha = 9.98804496392
Height: hb = 3.99221798557
Height: hc = 3.62992544142

Median: ma = 10.32198837203
Median: mb = 6.59554529791
Median: mc = 5.26878268764

Inradius: r = 1.59768719423
Circumradius: R = 5.51107737615

Vertex coordinates: A[11; 0] B[0; 0] C[1.68218181818; 3.62992544142]
Centroid: CG[4.22772727273; 1.21097514714]
Coordinates of the circumscribed circle: U[5.5; -0.34444233601]
Coordinates of the inscribed circle: I[2.5; 1.59768719423]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.7220033532° = 158°43'12″ = 0.37114054796 rad
∠ B' = β' = 114.8633288167° = 114°51'48″ = 1.13768500854 rad
∠ C' = γ' = 86.41766783015° = 86°25' = 1.63333370886 rad

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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 = 4 ; ; b = 10 ; ; c = 11 ; ;

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

p = a+b+c = 4+10+11 = 25 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 25 }{ 2 } = 12.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12.5 * (12.5-4)(12.5-10)(12.5-11) } ; ; T = sqrt{ 398.44 } = 19.96 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 19.96 }{ 4 } = 9.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 19.96 }{ 10 } = 3.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 19.96 }{ 11 } = 3.63 ; ;

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{ 4**2-10**2-11**2 }{ 2 * 10 * 11 } ) = 21° 16'48" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 10**2-4**2-11**2 }{ 2 * 4 * 11 } ) = 65° 8'12" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 11**2-4**2-10**2 }{ 2 * 10 * 4 } ) = 93° 35' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 19.96 }{ 12.5 } = 1.6 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 21° 16'48" } = 5.51 ; ;




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