Math Problem Statement
Solution
This problem involves using the Pythagorean Theorem to determine the height of the ladder against the house. The Pythagorean Theorem states:
Where:
- is one leg of the triangle (3 feet, the base of the ladder),
- is the other leg of the triangle (, the vertical height against the house),
- is the hypotenuse (10 feet, the length of the ladder).
Step 1: Plug in the known values
Step 2: Solve for
Step 3: Solve for
Final Answer:
Let me know if you want further details or explanations. Here are 5 related questions for further exploration:
- What would be the height if the base of the ladder was 4 feet away from the house?
- How does the Pythagorean Theorem apply to real-world problems like this one?
- What safety recommendations might apply when placing a ladder at different angles?
- How can you calculate the angle of the ladder using trigonometry?
- What is the area of the triangle formed by the ladder, house, and ground?
Tip: Always make sure your ladder is placed at a safe angle, which is often recommended as 75 degrees to the ground.
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Math Problem Analysis
Mathematical Concepts
Geometry
Trigonometry
Formulas
a^2 + b^2 = c^2 (Pythagorean Theorem)
Theorems
Pythagorean Theorem
Suitable Grade Level
Grades 7-9
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