Question

Britney is mapping out a new running path around her local park. She is going to run west for 2.1 km, before turning 105" to the night and running another 3.3 km From there, she will run in a straight line back to her starting position. How far will Britney run in total? Give your answer correct to the nearest meter.​

Answer 1

Britney will run approximately 9,090 meters in total.

Explanation:

To solve the problem, we can use the Law of Cosines to find the distance of the final straight line back to her starting position.

Let A be the starting position, B be the end of the first leg, and C be the end of the second leg. Then, we have:

AB = 2.1 km BC = 3.3 km ∠ABC = 180° - 105° = 75°

Using the Law of Cosines, we have:

AC² = AB² + BC² - 2(AB)(BC)cos(∠ABC)

AC² = (2.1)² + (3.3)² - 2(2.1)(3.3)cos(75°) AC ≈ 3.69 km

Therefore, Britney will run a total distance of approximately:

2.1 km + 3.3 km + 3.69 km ≈ 9.09 km

So, Britney will run approximately 9,090 meters in total.