11 15 16 triangle

Acute scalene triangle.

Sides: a = 11   b = 15   c = 16

Area: T = 79.37325393319
Perimeter: p = 42
Semiperimeter: s = 21

Angle ∠ A = α = 41.41096221093° = 41°24'35″ = 0.72327342478 rad
Angle ∠ B = β = 64.41769980226° = 64°25'1″ = 1.12442887097 rad
Angle ∠ C = γ = 74.17333798681° = 74°10'24″ = 1.2954569696 rad

Height: ha = 14.43113707876
Height: hb = 10.58330052443
Height: hc = 9.92215674165

Median: ma = 14.5
Median: mb = 11.5
Median: mc = 10.44403065089

Inradius: r = 3.78796447301
Circumradius: R = 8.31552184062

Vertex coordinates: A[16; 0] B[0; 0] C[4.75; 9.92215674165]
Centroid: CG[6.91766666667; 3.30771891388]
Coordinates of the circumscribed circle: U[8; 2.26877868381]
Coordinates of the inscribed circle: I[6; 3.78796447301]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.5990377891° = 138°35'25″ = 0.72327342478 rad
∠ B' = β' = 115.5833001977° = 115°34'59″ = 1.12442887097 rad
∠ C' = γ' = 105.8276620132° = 105°49'36″ = 1.2954569696 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 = 11 ; ; b = 15 ; ; c = 16 ; ;

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

p = a+b+c = 11+15+16 = 42 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 42 }{ 2 } = 21 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21 * (21-11)(21-15)(21-16) } ; ; T = sqrt{ 6300 } = 79.37 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 79.37 }{ 11 } = 14.43 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 79.37 }{ 15 } = 10.58 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 79.37 }{ 16 } = 9.92 ; ;

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{ 11**2-15**2-16**2 }{ 2 * 15 * 16 } ) = 41° 24'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-11**2-16**2 }{ 2 * 11 * 16 } ) = 64° 25'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-11**2-15**2 }{ 2 * 15 * 11 } ) = 74° 10'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 79.37 }{ 21 } = 3.78 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 41° 24'35" } = 8.32 ; ;




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