You are buiding a slide on a playground. The length of the slide is 15 feet and the top of the slide is 10 feet high. The angle formed by the slide and the ground should be between 30 to 50 degrees. Which of the following statements is correct?Select one:a.The angle formed by the slide and the ground is outside the range.b.The angle formed by the slide and the ground is within the given range.
Question
You are buiding a slide on a playground. The length of the slide is 15 feet and the top of the slide is 10 feet high. The angle formed by the slide and the ground should be between 30 to 50 degrees. Which of the following statements is correct?Select one:a.The angle formed by the slide and the ground is outside the range.b.The angle formed by the slide and the ground is within the given range.
Solution
To answer this question, we need to use the concept of trigonometry. Specifically, we'll use the sine function, which is defined as the ratio of the length of the side that is opposite the angle to the length of the longest side of the triangle (the hypotenuse).
In this case, the length of the slide is the hypotenuse, and the height of the slide is the side opposite the angle. So, we can calculate the sine of the angle as follows:
sin(angle) = opposite / hypotenuse = height / length = 10 feet / 15 feet = 0.6667
Now, we need to find the angle whose sine is 0.6667. We can do this using the arcsine function, which is the inverse of the sine function. Using a calculator, we find that:
angle = arcsin(0.6667) = 41.81 degrees
This angle is within the given range of 30 to 50 degrees. Therefore, the correct answer is:
b. The angle formed by the slide and the ground is within the given range.
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