ELS OLA Math Assignment Help From E . Numerade
C ezatest.com/testing/version1/olaViewer.html M Inbox (248) – miqua… New folder ??,” ELS Online Assessment Signed in as Miquan Jones Log Out Directions 8.G.1-8 Save Answer A playground slide and its vertical ladder form a right triangle with the ground. The slide itself is 15 feet long, and its bottom end is 12 feet from the ladder’s base. How tall is the slide’s ladder, in feet? feet Choice Blocker Highlight Line Viewer Ruler Ruler (Grades 2\&3) Protractor Calc Basic Calc Sci. Reference Desmos Graphing Calc
The Correct Answer and Explanation is:
To solve this problem, we can use the Pythagorean Theorem, a fundamental principle in geometry used to find the sides of a right triangle.
Given:
- The slide forms the hypotenuse of the triangle and is 15 feet long.
- The horizontal distance from the bottom of the slide to the base of the ladder (the base of the triangle) is 12 feet.
- We are asked to find the height of the ladder, which represents the vertical leg of the right triangle.
Step-by-step Solution Using the Pythagorean Theorem:
The Pythagorean Theorem states: a2+b2=c2a^2 + b^2 = c^2
Where:
- aa = one leg (the height we are solving for)
- bb = the other leg (12 feet)
- cc = the hypotenuse (15 feet)
Now, plug in the known values: a2+122=152a^2 + 12^2 = 15^2 a2+144=225a^2 + 144 = 225
Subtract 144 from both sides: a2=225−144=81a^2 = 225 – 144 = 81
Take the square root of both sides: a=81=9a = \sqrt{81} = 9
✅ Final Answer: The ladder is 9 feet tall.
Explanation:
This math problem involves a real-world application of the Pythagorean Theorem, which is essential in understanding right triangles. A right triangle has one angle that measures 90 degrees. The three sides of such a triangle are: two legs (shorter sides) and the hypotenuse (the longest side, opposite the right angle).
In this problem, the slide forms the hypotenuse of the triangle, the horizontal ground from the base of the slide to the ladder is one leg, and the vertical ladder is the other leg. The problem gives the hypotenuse as 15 feet and the base as 12 feet. Using the Pythagorean Theorem, we set up the equation: a2+122=152a^2 + 12^2 = 15^2
This becomes: a2+144=225a^2 + 144 = 225
Subtracting 144 from both sides isolates a2a^2, resulting in: a2=81a^2 = 81
Taking the square root gives us the answer: a=9a = 9. Therefore, the vertical height of the ladder is 9 feet.
This method is reliable for any scenario involving right triangles, such as in construction, navigation, or design. Understanding how to apply the Pythagorean Theorem helps students connect classroom math to real-life situations, enhancing both problem-solving skills and spatial reasoning.
