A toddler’s playground has two slides on either side. The slide on the left is situated at a 45° angle to the ground and is 68 centimeters away from the base of the playground. The slide on the right is positioned at a 30° angle to the ground and is 112 centimeters away from the playground’s base. What is the total length of both slides on this playground rounded to the nearest tenth of a centimeter?
225.5 or 104.1
To find the total length of both slides on the playground, we can use the concept of trigonometry. Let's calculate the length of each slide and then add them together:
1. Slide on the left:
The angle of the slide is 45°, and the distance from the base is 68 centimeters. We can use trigonometric functions, such as sine or cosine, to find the length of the slide.
Since the angle is between the height of the slide and the hypothenuse (the slide itself), we can use the sine function. The formula is:
sin(angle) = height / length of the slide
Rearranging the formula to solve for the length of the slide:
length of the slide = height / sin(angle)
length of the slide = 68 / sin(45°)
2. Slide on the right:
The angle of the slide is 30°, and the distance from the base is 112 centimeters. Again, using trigonometry, we can find the length of this slide. This time, we will use the cosine function since the angle is between the distance from the base and the hypothenuse.
Cosine function formula:
cos(angle) = base / length of the slide
Rearranging the formula:
length of the slide = base / cos(angle)
length of the slide = 112 / cos(30°)
To calculate the total length, we add the length of the slide on the left and the length of the slide on the right:
total length = length of the slide on the left + length of the slide on the right
Using a calculator, we can now plug in the values and perform the calculations to get the total length rounded to the nearest tenth of a centimeter.