Trigonometric Grade 11 Problem Solving?
Two hikers leave an intersection at the same time. One walks east at 6 km/h and the other walks northeast at 7.5 km/h. How far are the hikers apart after two hours, to the nearest tenth of a km?
Can someone explain how to do this to me please
- 1 decade agoFavorite Answer
First draw the directions, I recommand you draw them as vectors (like arrows):
- North points to the top
- South points to the bottom
- East points to the right
- West points to the left
Now lets draw a line from the center of your "+"-sign at about a 45 degree angle to the top right.
This is the hiker that travels northeast. Now the next hiker is simple, you just draw a line from the center to the east. That would be a straight line.
Now we assume that the angle between the two hikers is 45 degrees. Because that's one piece of the given information.
Let's calculate how far the first hiker has traveled: 7,5 x 2 = 15 km.
Let's calculate how far the second hiker has traveled: 6 x 2 = 12 km.
Now we can use sine to calculate the distance between the two hikers.
Note: please set your calculator on degrees. We call hiker's distance: x.
sin(45) = x / 15
15 * sin(45) = x
Now we know the distance between the two hikers.