the chains on a swing are 3.2m long and the seat is 0.5m off the ground when it is in the vertical position. When the swing is pulled as far back as possible, the chains make an angle of 40 degrees with the vertical. How high off the ground, to the nearest cm, is the seat when it is at this extreme position
Question
the chains on a swing are 3.2m long and the seat is 0.5m off the ground when it is in the vertical position. When the swing is pulled as far back as possible, the chains make an angle of 40 degrees with the vertical. How high off the ground, to the nearest cm, is the seat when it is at this extreme position
Solution
To solve this problem, we need to use some trigonometry. Here are the steps:
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First, we need to find the length of the chain from the top of the swing to the seat when the swing is at the extreme position. We can use the cosine of the angle to find this length. The cosine of an angle in a right triangle is equal to the adjacent side (which is the length we're trying to find) divided by the hypotenuse (which is the length of the chain). So, we have:
cos(40) = adjacent/hypotenuse cos(40) = adjacent/3.2m adjacent = 3.2m * cos(40)
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Next, we need to find the height of the seat from the ground when the swing is at the extreme position. This is equal to the length of the chain minus the length from the top of the swing to the seat. So, we have:
height = 3.2m - adjacent
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Finally, we need to add the height of the seat when the swing is in the vertical position (0.5m) to the height we just found to get the total height off the ground. So, we have:
total height = height + 0.5m
Now, we just need to plug in the numbers and do the calculations.
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