Kyle is pulled back on a swing so that the rope forms an angle of 30° with the vertical. The distance from the top of the swing set directly to the ground is 12 feet. Find Kyle’s height off the ground, x, when he is in the pulled-back position. Round the answer to the nearest hundredth.

Answers

Answer 1

Answer:

When Kyle is in the pulled-back position with the rope forming a 30° angle with the vertical, his height off the ground is 6 feet.

To find Kyle's height off the ground, x, when he is in the pulled-back position, we can use trigonometry.

First, let's draw a diagram to visualize the situation.

The swing set is represented by a vertical line, and the rope forms an angle of 30° with the vertical.

The distance from the top of the swing set to the ground is given as 12 feet.

Now, we can use the concept of sine to solve for Kyle's height off the ground.

The sine of an angle is equal to the length of the opposite side divided by the length of the hypotenuse.

In this case, the height off the ground is the opposite side, and the hypotenuse is the distance from the top of the swing set to the ground.

So, we can set up the following equation: sin(30°) = x / 12

To find x, we can multiply both sides of the equation by 12: 12 * sin(30°) = x

Using a calculator, we can find that sin(30°) is equal to 0.5: 12 * 0.5 = x Simplifying the equation: 6 = x

Therefore, Kyle's height off the ground, x, when he is in the pulled-back position, is 6 feet.

In summary, when Kyle is in the pulled-back position with the rope forming a 30° angle with the vertical, his height off the ground is 6 feet.

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Answer 2

Answer: This would be 12 - 12*cos(30) = 12 - 6 $√(3)$ = 1.608 ft off the ground.

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Answers

Answer:

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Answers

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Answers

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Answers

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