GED Mathematical Reasoning TestQuantitative Problem Solving with MeasurementMedium
A technician is installing a new security camera on a pole. The camera is 24 feet above the ground, and a sensor needs to be placed 7 feet away from the base of the pole on the ground. What is the straight-line distance between the camera and the sensor?
- A28 feet
- B31 feet
- C23 feet
- D25 feet
Show answer & explanationAnswer & explanation
Correct answer: D. 25 feet
This scenario forms a right-angled triangle where the pole is one leg (24 ft), the distance on the ground is the other leg (7 ft), and the straight-line distance is the hypotenuse. Using the Pythagorean theorem (a² + b² = c²): 7² + 24² = c² → 49 + 576 = c² → 625 = c² → c = √625 = 25 feet.
Why the other options are wrong
- A. This is incorrect; 28² = 784, not 625.
- B. This is incorrect; 31² = 961, not 625.
- C. This is incorrect; 23² = 529, not 625.
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 (legs).
- Formula: a² + b² = c²
- Only applies to right-angled triangles
- Used to find an unknown side length when two sides are known
Memory trick: A squared plus B squared equals C's grand prize!