A 30m high tower is supported by 4 ropes. The ropes are tied 5m from the top of the tower to four points on the ground. Each rope makes an angle of 60° with the ground. a Assuming the ropes do not sag, find the length of each one. b If 3% extra rope is needed to allow for sagging and tying, how much rope is needed to tie down the tower?

Step-by-step explanation:

Each rope forms a right angle triangle with the tower and the ground. The height which the rope makes with the tower represents the opposite side while the length of each rope represents the hypotenuse of the right angle triangle.

a) To determine the length, L of each rope, we would apply the sine trigonometric ratio which is expressed as

Sin θ = opposite side/hypotenuse. Therefore,

Opposite side = 30 - 5 = 25 m

Sin 60 = 25/L

L = 25/Sin60 = 25/0.866

L = 28.868m

b) The length of the 4 ropes is

28.868 × 4 = 115.5m

If 3% extra rope is needed to allow for sagging and tying, then the extra length needed is

3/100 × 115.5 = 3.465m

The length of rope needed to tie down the tower is

115.5 + 3.465 = 118.97 m

step-by-step explanation:

it has the same slope and a different y-intercept

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