ASVAB (Armed Services Vocational Aptitude Battery)Mathematics Knowledge (MK)Hard
A soldier is setting up a field communication antenna. A 25-foot cable runs from the top of a 20-foot mast to an anchor point on the ground. How far from the base of the mast is the anchor point, assuming the mast is perpendicular to the ground?
- A18 feet
- B15 feet
- C13 feet
- D10 feet
Show answer & explanationAnswer & explanation
Correct answer: B. 15 feet
This forms a right-angled triangle. The cable is the hypotenuse (c=25), the mast is one leg (a=20), and the distance to the anchor is the other leg (b). Using the Pythagorean theorem (a² + b² = c²): 20² + b² = 25² => 400 + b² = 625 => b² = 625 - 400 => b² = 225 => b = √225 = 15 feet.
Why the other options are wrong
- A. Significant calculation error.
- C. Possible error in squaring or square root calculation.
- D. Incorrect calculation or misidentified sides of the triangle.
Pythagorean Theorem (Finding a Leg)
In a right-angled triangle, if the hypotenuse and one leg are known, the other leg can be found using the Pythagorean theorem by rearranging the formula.
- Formula: a² + b² = c² (where c is hypotenuse).
- To find a leg: a² = c² - b² or b² = c² - a².
- Ensure correct identification of hypotenuse and legs.
Memory trick: Hypotenuse 'H'as 'S'quares, 'L'eg 'L'ooks for 'D'ifference.