Answer :-
9(3+√3) feet
Step by step explanation :-
A triangle is given to us. In which one angle is 30° and length of one side is 18ft ( hypontenuse) .So here we can use trignometric Ratios to find values of rest sides. Let's lable the figure as ∆ABC .
Now here the other angle will be = (90°-30°)=60° .
In ∆ABC ,
=> sin 30 ° = AB / AC
=> 1/2 = AB / 18ft
=> AB = 18ft/2
=> AB = 9ft .
Again In ∆ ABC ,
=> cos 30° = BC / AC
=> √3/2 = BC / 18ft
=> BC = 18 * √3/2 ft
=> BC = 9√3 ft .
Hence the perimeter will be equal to the sum of all sides = ( 18 + 9 + 9√3 ) ft = 27 + 9√3 ft = 9(3+√3) ft .
Hence the perimeter of the triangular pathway shown is 9 ( 3 + √3 ) ft .