Question about Mathematical Concepts

11. You are driving into St. Louis, Missouri, and in the distance you see the famous Gateway-to-the-West arch. This monument rises to a height of 192 m. You estimate your line of sight with the top of the arch to be 2.0° above the horizontal. Approximately how far (in kilometers) are you from the base of the arch?

The correct answer is 5.5 kilometers. I was wondering how did they get this result as the correct answer. Please show your work. Thanks.

21. A force vector F1 points due east and has a magnitude of 200 newtons. A second force F2 is added to F1. The resultant of the two vectors has a magnitude of 400 newtons and points along the east/west line. Find the magnitude and direction of F2. Note that there are two answers.

The correct answer is 200 N due east or 600 N due west. I was wondering how did they get this result as the correct answer. Please show your work. Thanks.

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