A point X is 34m due east of Y The bearing of fiyingpole from X and Y And N 18W andN40E respectively what is the distance of flagpole from Y pls with diagram and translation
Do you have the information to do it yourself? If not pay attention harder in your class.
Draw triangle XYZ where the flagpole is at Z. You have all the angles, so use the law of sines. YZ is side x (opposite angle X) so
x/sinX = z/sinZ
x/sin72° = 34/sin58°
To determine the distance of the flagpole from point Y, we first need to understand the bearing notation that is given in the question.
The bearing 18°W means that the flagpole is 18 degrees west of north (N). The bearing N40°E means that point Y is 40 degrees east of north (N).
Let's start by drawing a diagram to visualize the scenario:
N (North)
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---------Y--------------X-----------
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(Flagpole)
Now, we can analyze the information provided in the question. Point X is 34m due east of Y, so we can draw a line segment from Y to X, which is 34m long.
To find the distance of the flagpole from Y, we need to extend the line segment XY in the direction of point Y's bearing, which is N40°E. We can do this by drawing a line segment of an appropriate length in the N40°E direction from point X.
Remember that the bearing N40°E means a direction that is 40 degrees east of north. So, we need to turn clockwise 40 degrees from the north direction and then proceed in that direction.
Now, to determine the length of the line segment extending from X towards point Y's bearing, we can use basic trigonometry. We have a right-angled triangle formed by line segment XY as the base, and the line segment extending in the N40°E direction from X as the hypotenuse.
We are given the angle (40°) and the length of the base (34m). So we can use the trigonometric function tangent (tan) to find the length of the hypotenuse.
Using the formula:
tan(angle) = opposite/adjacent
We have:
tan(40°) = opposite/34m
To find the length of the opposite side (the distance from X to the flagpole), we rearrange the formula:
opposite = tan(40°) * 34m
Using a calculator, we find that tan(40°) is approximately 0.839. So:
opposite = 0.839 * 34m
opposite ≈ 28.626m
Therefore, the distance from the flagpole to point Y is approximately 28.626m.
In summary, the flagpole is approximately 28.626m away from point Y in the direction of N40°E.