From a part Z 60m north of X a man walk eastward to another point Y, 120m from X find the bearing of Y and X.
If θ is the bearing of Y from X, then
cosθ = 1/2
060
To find the bearing of point Y from point X, we can use trigonometry.
Step 1: Draw a diagram to visualize the problem.
Let's draw a straight line with point X at one end and point Y at the other end. Point Z is located 60m north of point X.
Z --------- X-----------------Y
60m 120m
Step 2: Calculate the distances and angles.
The distance between points X and Y is 120m.
Step 3: Determine the direction and angle.
Since the man walks eastward from point Z to point Y, we know that the bearing of Y from X is an angle measured clockwise from the north direction.
To find the bearing, we can use the tangent function.
Tangent(angle) = perpendicular/base
The perpendicular distance is 120m (the distance between points X and Y).
The base distance is 60m (the distance between points X and Z).
So, the tangent of the angle is 120/60 = 2.
Step 4: Calculate the angle.
To find the angle, we can take the inverse tangent (arctan) of 2 using a calculator.
arctan(2) ≈ 63.43°
Therefore, the bearing of point Y from point X is approximately 63.43° measured clockwise from the north direction.
To find the bearing of point Y from point X, we can use the concept of trigonometry. Given that the man walks eastward from point Z to point Y, we can construct a right-angled triangle with the hypotenuse as the 120m distance between X and Y, the adjacent side as the 60m distance between Z and X, and the opposite side as the unknown distance between Z and Y.
Using the trigonometric function tangent, we can determine the angle between the east direction and the line connecting X and Y. The tangent function is defined as the ratio of the opposite side to the adjacent side.
In this case, the tangent of the angle can be calculated as:
tan(θ) = opposite side / adjacent side
tan(θ) = unknown distance / 60m
Now, we can rearrange the equation to solve for the unknown distance:
unknown distance = tan(θ) * 60m
To find the angle θ, we can calculate it as:
θ = arctan(unknown distance / 60m)
Once we have the angle θ, we can convert it to a bearing. A bearing is typically measured clockwise from the north direction. Therefore, if we denote the north direction as 0°, east direction as 90°, south direction as 180°, and west direction as 270°, we can convert the angle θ to a bearing by adding 90° (to adjust for the eastward direction) and then take the result modulo 360° (to ensure the bearing is within the range of 0° to 360°).
Bearing = (θ + 90°) % 360°
By following this process, you can determine the bearing of point Y from point X.