Solve each problem. See Examples 1 and 2.

Distance Traveled by a...

Question

Solve each problem. See Examples 1 and 2.

Distance Traveled by a Ship A ship travels 55 km on a bearing of 27° and then travels on a bearing of 117° for 140 km. Find the distance from the starting point to the ending point.

Accepted Answer

A tourist walking in the desert walks 33 kilometers on a bearing of 53 degrees and then 75 kilometers on a bearing of 143 degrees. Find the distance between the end point and the initial starting point of the tourist. Now, we have four possible answers, all measures and kilometers to solve this. Let's first make a diagram. Our first point point A will be where the tour starts and the tourist moves in the barn at 53 degrees for kilometers. Now, this is referenced from the north and the clockwise direction so we can draw an angle going 53 degrees from the north that is 33 kilometers. Now, we'll be at point B and here the tourist moves 75 kilometers at 143 degrees from the north. So we can draw another angle going 143 degrees and then we can draw a new vector for kilometers. This goes to point C. Finally, we will connect points A and C with a single vector. Now, let's see if this right here is a right triangle. We can make a supplementary angle for 1 43 which should be 37 degrees. We can also say our missing angle here is 53 degrees, those two angles add to 90 which confirm we have a right triangle. We can then use Pythagorean theorem to solve our Mystic side KC. We look at AC squared as equals to A B squared and BC squared added together. No, we will get AC squared as equals to 33 squid plus 75 square. This gives us AC squared. It's equals to 67 14. You take the square root of both sides to get AC is approximately 81.94 kilometers. We then see the answer to our problem. This answer D OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

Solve each problem. See Examples 1 and 2. Distance Traveled by a Ship A ship travels 55 km on a bearing of 27° and then travels on a bearing of 117° for 140 km. Find the distance from the starting point to the ending point.

Key Concepts

Bearings

Law of Cosines

Vector Addition

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