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

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.

7

step-by-step explanation:

the answer would be 7