11 17 18 triangle

Acute scalene triangle.

Sides: a = 11   b = 17   c = 18

Area: T = 90.99545053286
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 36.49437665998° = 36°29'38″ = 0.63769363836 rad
Angle ∠ B = β = 66.88001568171° = 66°48'1″ = 1.16658826773 rad
Angle ∠ C = γ = 76.70660765831° = 76°42'22″ = 1.33987735927 rad

Height: ha = 16.54444555143
Height: hb = 10.7055235921
Height: hc = 10.11105005921

Median: ma = 16.62107701386
Median: mb = 12.25876506721
Median: mc = 11.13655287257

Inradius: r = 3.95662828404
Circumradius: R = 9.24878111394

Vertex coordinates: A[18; 0] B[0; 0] C[4.33333333333; 10.11105005921]
Centroid: CG[7.44444444444; 3.3770166864]
Coordinates of the circumscribed circle: U[9; 2.12765020267]
Coordinates of the inscribed circle: I[6; 3.95662828404]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.50662334° = 143°30'22″ = 0.63769363836 rad
∠ B' = β' = 113.2199843183° = 113°11'59″ = 1.16658826773 rad
∠ C' = γ' = 103.2943923417° = 103°17'38″ = 1.33987735927 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 = 17 ; ; c = 18 ; ;

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

p = a+b+c = 11+17+18 = 46 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 46 }{ 2 } = 23 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23 * (23-11)(23-17)(23-18) } ; ; T = sqrt{ 8280 } = 90.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 90.99 }{ 11 } = 16.54 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 90.99 }{ 17 } = 10.71 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 90.99 }{ 18 } = 10.11 ; ;

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**2-17**2-18**2 }{ 2 * 17 * 18 } ) = 36° 29'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-11**2-18**2 }{ 2 * 11 * 18 } ) = 66° 48'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-11**2-17**2 }{ 2 * 17 * 11 } ) = 76° 42'22" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 90.99 }{ 23 } = 3.96 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 36° 29'38" } = 9.25 ; ;




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