Question

To get from her home to Grandma's house, Red Riding Hood drove due north 120 miles, then turned left and drove due west and additional 40 miles, How far, as the crow flies, is Red's house from Grandma's house? (Round your answer to the nearest mile).

Answer 1

To find the distance as the crow flies between Red Riding Hood's and Grandma's house, we use the Pythagorean theorem. After calculating the hypotenuse of the right triangle created by the two legs of the trip (120 miles north and 40 miles west), we determine the straight-line distance to be approximately 126 miles.

Step-by-step explanation:

This is asking about that involves calculating the straight-line distance, also known as the crow flies distance, between two points after a displacement that includes two legs at right angles to each other. This is a typical problem that can be solved using the Pythagorean theorem. Red Riding Hood first drives 120 miles north and then turns left to drive 40 miles west. To find the straight-line distance from Red's house to Grandma's house, we represent these two segments as perpendicular sides of a right triangle and calculate the hypotenuse. Using the Pythagorean theorem, c^2 = a^2 + b^2, where 'c' is the hypotenuse (the distance as the crow flies), and 'a' and 'b' are the other two sides of the triangle. Plugging in the values: a = 120 miles, b = 40 miles. We get c^2 = 120^2 + 40^2 = 14400 + 1600 = 16000. Thus, c = √16000 = 126.49. When rounded to the nearest mile, the distance as the crow flies is 126 miles.