a stuntman uses a 30 foot rope to swing 120 degrees between two platforms of equal height, grazing the ground in the middle of the swing. If the rope stays taut throughout the swing, how far above the ground was the stuntman at the beginning and the end of the swing? How far apart were the two platforms? Round your answer to the nearest two decimal places.

15ft

51.96ft

Step-by-step explanation:

A = start point of the swing

B = end point of the swing

a = height off the ground at A and B

b = distance between start and end point = 2d

c = vertical height of the point of swinging above the start or end point

h = height of the point of swinging from the lowest point of swing (when the rope is vertical)  = length of the rope

h = 30

Firstly, we can see from the image:

a = h - c

We know h = 30, so we just need to know c;

A right angle triangle can be constructed as can be seen on the image I've drawn;

We can use trigonometry, specifically the cosine function, to find c:

cos(θ) = adjacent/hypotenuse

cos(60) = c/30

c/30 = ¹/₂

c = 30(¹/₂)

c = 15

∴ a = 30 - 15

a = 15ft

For the second part, to find b;

We can use the sine function to find d:

sin(60) = d/30

d/30 = ¹/₂(√3)

d = 15√3

b = 2d

b = 2(15√3)

b = 30√3 = 51.96... ⇒ 51.96ft

∠cbe and ∠deb are same-side interior angles.

i took the test