You walk 50 m to the north, then turn 60° to your right and walk another 45 m. How far are you from where you originally started?
well if you start 50 m Due South of the North Pole,it makes a very interesting problem. Think on that.
Now anywhere else,
result= 50N+ 45sin60 E + 45 cos60 N
then combine the like directons, and the distance will be given by the distance formula
distance= sqrt (xN^2 + yE^2) where xN is the north distance, and yE is the east distance
63 m
To determine how far you are from where you originally started, we can visualize the scenario using a diagram and then use trigonometry to solve for the final distance. Here's how we can do it step by step:
Step 1: Start by drawing a diagram to represent the situation. Draw a straight line to represent the initial distance of 50 m to the north. Then, draw a right angle where the line ends to signify your turning point. Finally, draw another line at a 60° angle to the right, representing the additional 45 m you walked.
| 45 m
|_________
| /
50 m | /
N | /
|/
Step 2: Now, we can consider the triangle formed by the initial 50 m line, the additional 45 m line, and the straight line connecting the starting point and the final destination.
Step 3: To find the perpendicular distance between the initial starting point and the final destination, we need to determine the opposite side of the triangle (OP in the diagram) that is perpendicular to the original direction of the walk.
Step 4: Using trigonometry, we see that OP is the product of the sine of the angle and the length of the additional 45 m line. OP = sin(60°) * 45 m.
Step 5: Calculate the value of sin(60°). sin(60°) = √3/2.
Step 6: Substitute this value into the equation: OP = (√3/2) * 45 m.
Step 7: Simplify the equation: OP = (√3 * 45)/2 = (45√3)/2.
Step 8: Now, we have the opposite side (OP) of the triangle, which represents the perpendicular distance between the starting point and the final destination. To get the total distance, we add the opposite side (OP) to the initial 50 m distance.
Step 9: Total distance = 50 m + (45√3)/2 m.
Step 10: Approximating the value of √3 as 1.73, we can calculate the total distance using the formula:
Total distance = 50 m + (45 * 1.73)/2 m.
Step 11: By substituting the given values, we have:
Total distance = 50 m + 77.17 m ≈ 127.17 m.
Therefore, you are approximately 127.17 m away from where you originally started.