The vertical slide ladder at the community swimming pool is 12.5 meters tall. The angle created by the top of the ladder and the top of the slide is 38°. Find the approximate length of the swimming pool slide to the nearest hundredth.
The vertical slide ladder at the community swimming pool is 12.5 meters tall. The angle created by the top of the ladder and the top of the slide is 38°. Find the approximate length of the swimming pool slide to the nearest hundredth.
To find the length of the swimming pool slide, we can use trigonometry (specifically, the sine function). Here's how:
Step 1: Draw a diagram to visualize the problem. The vertical ladder forms a right triangle with the swimming pool slide. The angle between the ladder and the slide is 38°.
Step 2: Label the sides of the triangle. Let the height of the ladder (vertical side) be 'a' and the length of the slide (hypotenuse) be 'c'.
Step 3: Find the side lengths in terms of 'a'. From the given information, we know that the ladder is 12.5 meters tall, so we can label that as 'a = 12.5'.
Step 4: Use the sine function to find 'c'. The sine of an angle is defined as the ratio of the opposite side to the hypotenuse. In this case, the opposite side is 'a' and the hypotenuse is 'c'. Therefore, we have: sin(38°) = a/c.
Step 5: Solve for 'c'. Rearrange the equation from step 4 to solve for 'c': c = a / sin(38°).
Step 6: Plug in the values to find 'c'. Substitute the known values into the equation from step 5: c = 12.5 / sin(38°).
Step 7: Use a calculator to find the approximate value of 'c'. Evaluate the expression using a calculator to find the approximate length of the swimming pool slide. Round the answer to the nearest hundredth.
By following these steps, you can find the approximate length of the swimming pool slide.