Solve each problem. See Examples 1 and 2. Distance between Two...

Question

Solve each problem. See Examples 1 and 2. Distance between Two Cities The bearing from Atlanta to Macon is S 27° E, and the bearing from Macon to Augusta is N 63° E. An automobile traveling at 62 mph needs 1¼ hr to go from Atlanta to Macon and 1¾ hr to go from Macon to Augusta. Find the distance from Atlanta to Augusta.

Accepted Answer

The barren from P to Q is south 18 degrees east. The bearing from Q to R is north 72 degrees east. A cyclist riding at 20 MPH takes 2.25 hours to go from P to Q and 2.75 hours to go from Q to R, determine the distance from P to R. Now, we have four possible answers being 31.62 miles, 62.31 miles, 71.06 miles or 6.71 miles. Now, to solve this, let's first draw a picture. We'll first note point P. Now it tells us the bearing from P to Q is south to 18 degrees east. If we were the driver's angle, we would go to the south and go to the east 18 degrees. This gives us a vector going in the direction of south. 18 degrees east. We'll do the same for Q. Now we have Q and from Q to R, we have north 72 degrees east. So it's R, we will start from Q, go to the north and to the right by 72 degrees, you go over and make a vector in that direction. Now, we can draw point R and make a vector between point P and point R. You notice here we have a right triangle but we have degrees from P to Q and 72 degrees from Q to R those adds equal 90. So we have a right triangle. Now, we need to find a distance from P to R. Since this is a right triangle, we can just use Python theorem. But we first need our missing side links PQ and QR. Now we know what it tells us. It took 2.25 hours to go from P to Q at 20 MPH. We can then say 20 MPH multiplied by 2.25 hours, which gives us a distance for PQ of 45 miles. We can do the same for QR or you are, it tells us it's like 2.75 hours, which means we have 28 MPH multiplied by 2. hours. This gives us 55 miles. Now, we can use Pythagorean theorem to find our final side links. We would get pr squared as equals to PQ squared plus QR squared, which will be 45 squared plus 55 square. Now we take the square root of both sides to get pr we then get pr this equals the square root of 50 50 which is about 71.06 miles, we can then say the answer to our problem is answer. C ok. I hope to help you solve the problem. Thank you for watching. Goodbye.

Key Concepts

Bearing and Direction in Navigation

Distance, Speed, and Time Relationship

Law of Cosines for Non-Right Triangles

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