Digital SATMath: Geometry and TrigonometryEasy
A builder is constructing a ramp for wheelchair access. The ramp needs to rise 3 feet vertically over a horizontal distance of 4 feet. What is the length of the ramp surface?
- A3 feet
- B4 feet
- C5 feet
- D7 feet
Show answer & explanationAnswer & explanation
Correct answer: C. 5 feet
This scenario forms a right-angled triangle where the vertical rise is one leg (a=3), the horizontal distance is the other leg (b=4), and the ramp surface is the hypotenuse (c). Using the Pythagorean theorem (a² + b² = c²): 3² + 4² = c² -> 9 + 16 = c² -> 25 = c² -> c = √25 = 5 feet.
Why the other options are wrong
- A. This is the vertical rise, not the ramp length.
- B. This is the horizontal distance, not the ramp length.
- D. This is the sum of the vertical and horizontal distances, not the hypotenuse.
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.
- Only applies to right-angled triangles.
- Formula: a² + b² = c² (where a and b are legs, c is hypotenuse).
- Used to find an unknown side length.
Memory trick: Right triangle? Think 'A-squared plus B-squared equals C-squared' for sides.