Question

(Will give brainliest :) pls tell me how to solve) Hikers are traveling at 3 miles per hour. They leave camp and hike LaTeX: N64^\circ WN 64 ∘ W for 2 hours. They change course to LaTeX: S23^\circ WS 23 ∘ W for 4 hours. How many miles is the trip back to camp. What bearing should they take to head back to camp?

Answer 1

Answer:

3.08270264 hours

Step-by-step explanation:

The first thing you have to do is a graph where you signal the cardinal points (1st image)

Then draw the first line that the problem gives you (N64°W). At the end of this line, you will draw the following line (S23°W) drawing another little graph as a guide. Finally, you will draw the last line, as long as a triangle is made (2nd image)

If you pay attention to the first line you made, you will notice that you can make a right triangle with angles of 90°, 64°, and 26° (3rd image)

So, returning to the other big triangle, you are going to add the 23° of the main orientation with the 26° that you just obtained from the first triangle (4th image)

Now you have a large triangle with one side that is worth 4, another that is worth 2, and an angle between them that is worth 49° (5th image)

From now on it's easier.

We know that if we have an angle between two know sides we can use Law of cosines (a²=b²+c²-2bcCosA)

So a² = 2² + 4² - 2(2*4)Cos49

a² = 4 + 16 - 2(8)Cos49

a² = 20 - 16Cos49

Cos49 = 0.65605902899

16 * 0.65605902899 = 10.4969444638

20 - 10.4969444638 = 9.50305554

a² = 9.50305554

a = $\sqrt{9.50305554}$ = 3.08270264

Hope I helped you and sorry for the bad quality of the photos