A Point X is 34m due east of a point Y.The bearings of a flagpole from X and Y are N18degreeW N40degreeE respectively. Calculate the distance of the flagpole from Y
Draw the diagram. If we label the flag pole P, then in triangle XYP, we have
angle X = 72°, Y = 50°, so angle P=58° since they add up to 180°.
So, using the law of sines and the usual labeling of sides (p = side XY, opposite P),
y/sinY = p/sinP
So plug in your numbers.
34/sin58 = 40 m.
x/sin72 = 40
x =
y/sin50 = 40
y =
3.8
The answer is 38.1m
38.13m
To calculate the distance of the flagpole from point Y, we can use trigonometry.
First, let's label the points as follows:
Point X: (0, 0)
Point Y: (34, 0)
Flagpole location: (x, y)
We know that the bearing from X to the flagpole is N18°W, and the bearing from Y to the flagpole is N40°E.
To find the distance between Y and the flagpole, we need to determine the coordinates of the flagpole.
From the bearing N40°E, we know that the angle between the line connecting Y to the flagpole and the east direction is 40°. This means that the angle between the line connecting Y to the flagpole and the west direction is 180° - 40° = 140°.
Similarly, from the bearing N18°W, we know that the angle between the line connecting X to the flagpole and the west direction is 18°. This means that the angle between the line connecting X to the flagpole and the east direction is 180° - 18° = 162°.
Now, we can use trigonometry to calculate the coordinates of the flagpole.
For the x-coordinate of the flagpole, we can use the cosine function:
cos(162°) = (x - 34) / x
Simplifying the equation, we have:
x - 34 = x * cos(162°)
x - x * cos(162°) = 34
x * (1 - cos(162°)) = 34
x = 34 / (1 - cos(162°))
For the y-coordinate of the flagpole, we can use the sine function:
sin(162°) = y / x
Simplifying the equation, we have:
y = x * sin(162°)
Now, let's calculate the values:
- First, convert 18° and 40° to radian measure:
18° = 18 * π / 180 ≈ 0.31416 rad
40° = 40 * π / 180 ≈ 0.69813 rad
- Next, calculate the x-coordinate of the flagpole:
x = 34 / (1 - cos(162°))
x = 34 / (1 - cos(0.69813))
x ≈ 314.73 m
- Finally, calculate the y-coordinate of the flagpole:
y = x * sin(162°)
y = (314.73) * sin(0.31416)
y ≈ 101.27 m
Therefore, the distance of the flagpole from point Y is approximately 101.27 meters.