Question

Question A coast guard patrol boat and a fishing boat leave a dock at the same time on the courses shown. The patrol boat travels at a speed of 15 nautical miles per hour (15 knots), and the fishing boat travels at a speed of 2 knots. After 1 hour, the fishing boat sends a distress signal, which is picked up by the patrol boat. If the fishing boat does not drift, how long will it take the patrol boat to reach the fishing boat at a speed of 15 knots? Round the intermediate result to three decimal places and the final answer to the nearest thousandth. A diagram shows a triangle labeled Uppercase D Uppercase F Uppercase P. The side Uppercase D Uppercase F measures two. The side Uppercase D Uppercase P measures fifteen. The side Uppercase F Uppercase P is labeled as Lowercase d. A vertical dashed line extends up from the vertex D to a point N, forming an angle with side Uppercase D Uppercase P measuring twenty degrees. Angle Uppercase F Uppercase D Uppercase N measures one hundred five degrees. Enter the correct value in the box.

Answer 1

Let’s use the law of cosines to solve this problem. The law of cosines states that for any triangle with sides a, b, and c, and angle C opposite to side c, the following equation holds: c^2 = a^2 + b^2 - 2ab cos. In our case, we know that the patrol boat travels at a speed of 15 knots and the fishing boat travels at a speed of 2 knots. After 1 hour, the fishing boat sends a distress signal, which is picked up by the patrol boat. If the fishing boat does not drift, we can assume that it has traveled 2 nautical miles in one hour . Let’s call the distance between the patrol boat and the fishing boat “d”. We can use the law of cosines to solve for “d” as follows:

d^2 = 15^2 + 2^2 - 2(15)(2)cos(105°) d^2 = 225 + 4 - 60cos(105°) d^2 = 229.8 d ≈ 15.16 nautical miles

Therefore, it will take the patrol boat approximately 1.011 hours to reach the fishing boat at a speed of 15 knots .