A man walks at a steady course bearing 122 degrees from A to B. If A is 86 m further west than B, find (to the nearest metre) how far the man has walked.
X/Sin90 = 86/Sin58
X = 101.41m (2 d.p.)
To solve this problem, we can use the concept of trigonometry and the distance formula. Let's break down the steps to find the distance the man has walked:
Step 1: Draw a diagram
Draw two points on a coordinate plane representing points A and B. Label the coordinates of A as (x, y) and assume B is at the origin (0, 0).
Step 2: Determine the bearing
Since the man is walking at a bearing of 122 degrees, we can find the angle it makes with the x-axis. Subtract 90 degrees from 122, which gives us 32 degrees.
Step 3: Find the y-coordinate
Since the angle is relative to the x-axis, we can determine the y-coordinate of point A by calculating the length of the side opposite to the 32-degree angle. Let's use sine to find the y-coordinate of A:
y = distance * sin(angle)
where distance represents the distance from A to B.
Step 4: Find the x-coordinate
Using the information given in the problem, we know that A is 86 meters further west than B. So the x-coordinate of A is distance - 86.
Step 5: Calculate the distance between A and B
Now that we have the coordinates of points A and B, we can use the distance formula to find the distance between them:
distance = √(x2 - x1)^2 + (y2 - y1)^2
where (x1, y1) and (x2, y2) are the coordinates of A and B, respectively.
Step 6: Round the distance to the nearest meter
Finally, round the calculated distance to the nearest meter to get the desired answer.
By following these steps, you should be able to find the distance the man has walked.
draw a diagram. Clearly the distance x is found using
86/x = sin 36°