Praxis Core Academic Skills for Educators: Mathematics (5733)GeometryMedium
A painter is using a ladder to reach a window. The ladder is 13 feet long and its base is placed 5 feet away from the wall. Assuming the wall is perfectly vertical, how high up the wall does the ladder reach?
- A14 feet
- B12 feet
- C8 feet
- D10 feet
Show answer & explanationAnswer & explanation
Correct answer: B. 12 feet
This scenario forms a right-angled triangle where the ladder is the hypotenuse (c), the distance from the wall is one leg (a), and the height up the wall is the other leg (b). Using the Pythagorean theorem (a² + b² = c²): 5² + b² = 13². So, 25 + b² = 169. Subtracting 25 from both sides gives b² = 144. Taking the square root, b = 12 feet.
Why the other options are wrong
- A. This is an incorrect calculation, possibly 13 + 1.
- C. This is 13 - 5, which is incorrect for Pythagorean theorem.
- D. This is sqrt(100), but the calculation for b^2 is 144.
Pythagorean Theorem
In a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
- Applies only to right-angled triangles.
- Formula: a² + b² = c², where c is the hypotenuse.
- Can be used to find an unknown side length if two sides are known.
Memory trick: A squared plus B squared equals C squared, for right triangles, it's always declared!