(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?
Answers
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 = [tex]\sqrt{9.50305554}[/tex] = 3.08270264
Hope I helped you and sorry for the bad quality of the photos
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Step-by-step explanation:
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