Final answer:
To find the height of the stairs, we used the Pythagorean theorem to calculate the height difference, which was 8.49 feet, and then added the 2 feet difference from the end of the slide to get a total height of 10.49 feet for the stairs.
Step-by-step explanation:
In this mathematics problem, we are asked to find out how tall the stairs are at the playground Bobby visited. Given that the slide is 13 feet long and the end of the slide is 7 feet away from the stairs, we can visualize a right triangle where the slide represents the hypotenuse, the distance from the stairs to the end of the slide represents one leg, and the height of the stairs represents the other leg. We also know that the stairs are 2 feet higher than the end of the slide. We can use the Pythagorean theorem to solve for the height of the stairs.
First, we will subtract the 2 feet from the length of the slide to account for the height difference: 13 feet - 2 feet = 11 feet. This means the slide runs 11 feet along the vertical height of the stairs. Next, we apply the Pythagorean theorem (a² + b² = c²) using the vertical height and the distance between the end of the slide and the stairs (7 feet).
Now, we have a right triangle with one leg measuring 7 feet and the hypotenuse measuring 11 feet. We will calculate the length of the other leg (the height of the stairs), which we'll call 'h'.
7² + h² = 11²
49 + h² = 121
h² = 121 - 49
h² = 72
h = √72
After calculating the square root of 72, we find that h is approximately 8.49 feet. However, we must remember to add the original 2-foot difference in height back to get the total height of the stairs.
Hence, the total height of the stairs is about 8.49 feet + 2 feet = 10.49 feet. This answer can be rounded to the nearest whole number if needed, so the stairs are approximately 10 feet tall.