ASVAB (Armed Services Vocational Aptitude Battery)Mathematics Knowledge (MK)Hard
A communication specialist is installing a new antenna. The antenna mast is 12 feet tall, and a guy wire is anchored to the ground 5 feet away from the base of the mast. How long is the guy wire, assuming the mast is perpendicular to the ground?
- A13 feet
- B17 feet
- C14 feet
- D11 feet
Show answer & explanationAnswer & explanation
Correct answer: A. 13 feet
This forms a right-angled triangle where the mast is one leg (a=12), the distance to the anchor is the other leg (b=5), and the guy wire is the hypotenuse (c). Using the Pythagorean theorem (a² + b² = c²): 12² + 5² = c² => 144 + 25 = c² => 169 = c² => c = √169 = 13 feet.
Why the other options are wrong
- B. Simply added the two sides (12+5), ignoring the right angle relationship.
- C. Calculation error or incorrect application of the theorem.
- D. Incorrect calculation or misremembered Pythagorean triple.
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, where a and b are legs, c is hypotenuse.
- Applies only to right-angled triangles.
- Often used in geometry, construction, and navigation.
Memory trick: A 'S'quare 'S'um 'S'olves 'C'.