Digital SATMath: Geometry and TrigonometryMedium
A pilot is planning a short flight. The flight path involves flying 60 miles due east and then turning due north for 80 miles. What is the straight-line distance from the starting point to the final destination?
- A100 miles
- B140 miles
- C160 miles
- D120 miles
Show answer & explanationAnswer & explanation
Correct answer: A. 100 miles
This scenario forms a right-angled triangle where the eastward path (60 miles) and the northward path (80 miles) are the two legs, and the straight-line distance is the hypotenuse. Using the Pythagorean theorem (a² + b² = c²): 60² + 80² = c² -> 3600 + 6400 = c² -> 10000 = c² -> c = √10000 = 100 miles.
Why the other options are wrong
- B. This is the sum of the two legs (60+80), not the hypotenuse.
- C. This is an distractor, possibly from a calculation error or incorrect formula.
- D. This is an distractor, possibly from a calculation error or incorrect formula.
Pythagorean Triples
A set of three positive integers a, b, and c, such that a² + b² = c².
- Common triples include (3, 4, 5) and its multiples (e.g., 6, 8, 10).
- Useful for quickly solving right triangle problems on exams.
- Indicates a right-angled triangle.
Memory trick: For 'as the crow flies', think of a right triangle.