Question

Approximately how far north of Pigeon Lake was the cyclist when she was the greatest distance away from Pigeon Lake? At what time did this occur?

A) Use the Pythagorean Theorem to calculate distance
B) Use the Law of Cosines to calculate distance
C) Use trigonometry to calculate the angle
D) None of the above

Answer 1

To determine the cyclist's maximum distance from Pigeon Lake, we can use the Pythagorean theorem. The correct option is A) Use the Pythagorean Theorem to calculate distance.

Step-by-step explanation:

The correct option to answer this question is A) Use the Pythagorean Theorem to calculate distance.

To determine the cyclist's distance from Pigeon Lake, we can use the Pythagorean theorem.

1. First, we need to identify the two legs of the trip that form a right triangle.
2. Let's say the cyclist travels x kilometers north of Pigeon Lake, and the distance from Pigeon Lake to her location is y kilometers.
3. The straight-line distance is the hypotenuse of the right triangle, which we need to calculate using the Pythagorean theorem: x² + y² = c².
4. To find the maximum value of c (distance away from Pigeon Lake), we need to maximize the value of y.
5. This occurs when the cyclist is directly west of Pigeon Lake, so the angle between the cyclist's location and the straight-line distance is 90 degrees.
6. Using the Pythagorean theorem, we solve for y: y² = c² - x².
7. Substituting the known values and solving for y, we can find the maximum distance from Pigeon Lake.
8. To determine the time at which this occurs, we need additional information such as the cyclist's speed or the duration of her trip.