7 10 11 triangle

Acute scalene triangle.

Sides: a = 7   b = 10   c = 11

Area: T = 34.2932856399
Perimeter: p = 28
Semiperimeter: s = 14

Angle ∠ A = α = 38.57326508222° = 38°34'22″ = 0.67332197581 rad
Angle ∠ B = β = 62.96443082106° = 62°57'52″ = 1.09989344895 rad
Angle ∠ C = γ = 78.46330409672° = 78°27'47″ = 1.3699438406 rad

Height: ha = 9.79879589711
Height: hb = 6.85985712798
Height: hc = 6.23550647998

Median: ma = 9.91221138008
Median: mb = 7.74659666924
Median: mc = 6.65220673478

Inradius: r = 2.44994897428
Circumradius: R = 5.61334139939

Vertex coordinates: A[11; 0] B[0; 0] C[3.18218181818; 6.23550647998]
Centroid: CG[4.72772727273; 2.07883549333]
Coordinates of the circumscribed circle: U[5.5; 1.12326827988]
Coordinates of the inscribed circle: I[4; 2.44994897428]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.4277349178° = 141°25'38″ = 0.67332197581 rad
∠ B' = β' = 117.0365691789° = 117°2'8″ = 1.09989344895 rad
∠ C' = γ' = 101.5376959033° = 101°32'13″ = 1.3699438406 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 = 7 ; ; b = 10 ; ; c = 11 ; ;

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

p = a+b+c = 7+10+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 * (14-7)(14-10)(14-11) } ; ; T = sqrt{ 1176 } = 34.29 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 34.29 }{ 7 } = 9.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 34.29 }{ 10 } = 6.86 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 34.29 }{ 11 } = 6.24 ; ;

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{ 7**2-10**2-11**2 }{ 2 * 10 * 11 } ) = 38° 34'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 10**2-7**2-11**2 }{ 2 * 7 * 11 } ) = 62° 57'52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 11**2-7**2-10**2 }{ 2 * 10 * 7 } ) = 78° 27'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 34.29 }{ 14 } = 2.45 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 38° 34'22" } = 5.61 ; ;




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