Final answer:
To find the height of the top of the slide above the ground, we use the sine function of the given angle of 27 degrees multiplied by the length of the slide, which is the hypotenuse of the right-angled triangle formed by the slide.
Step-by-step explanation:
The question asks how high is the top of a slide above the ground, given that the slide is 4.1 meters long and makes an angle of 27 degrees with the ground. To solve this, we apply trigonometric principles, particularly the sine function, as the height of the slide corresponds to the opposite side in a right-angled triangle, where the slide itself represents the hypotenuse.
Step-by-Step Solution
Identify the given information: the length of the slide (hypotenuse) is 4.1 meters and the angle with the ground is 27 degrees.
Recognize that we need to find the length of the opposite side that represents the height.Use the sine function: height = hypotenuse × sin(angle).Calculate the height: height = 4.1 m × sin(27°).Use a calculator to find the sine of 27 degrees and multiply by 4.1 meters to get the final height.
- By performing these steps, you can find out how high the top of the slide is above the ground.