The perimeter of the right-angled triangle is 72.7 metres to 1 d.p.
Using trigonometry, we can solve for the perimeter of the right-angled triangle as follows:
Find the length of the hypotenuse using the sine function:
sin(32°) = 16.6 m / hypotenuse
hypotenuse = 16.6 m / sin(32°)
hypotenuse = 31.2 m
Find the length of the other leg using the cosine function:
cos(32°) = 16.6 m / other_leg
other_leg = 16.6 m / cos(32°)
other_leg = 24.9 m
Calculate the perimeter of the triangle by adding the lengths of the three sides:
perimeter = hypotenuse + other_leg + base
perimeter = 31.2 m + 24.9 m + 16.6 m
perimeter = 72.7 m