She should navigate at 45° 34' 22.7856" to go to Island C.
Given that Susan is on vacation at a tropical bay that has three islands, and she rents a boat on Island A and plans to navigate to Island C, which is 8 miles away, to determine, based on the figure below, at what angle should she navigate to go to Island C, the following calculation must be carried out, applying the cosine law:
- 11^2 = 8^2 + 15^2 - (2 x 8 x 15) x cos A
- Cos A = (8^2 + 15^2 - 11^2) / (2x8x15)
- A = arc cos (8^2 + 15^2 - 11^2) / (2x8x15)
- A = arc cos (64 + 225 - 121) / 240
- A = arc cos (168 / 240)
- A = arc cos 0.7
- A = 45.572996
Therefore, she should navigate at 45° 34' 22.7856" to go to Island C.
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