How to draw a a point x is 34m due east of point y. The bearing of a flag pole from x and y are N 18 W and N40E respectively. Calculate the distance of the flag pole from x and y
I assume you have some graph paper. Plot the points Y=(0,0) and X=(34,0)
Construct the two angles at X and Y, and their intersection will be at the pole, P.
Now, in triangle XYP, you have
X = 90-18 = 72°
Y = 90-40 = 50°
so Z = 58°
Now use the law of since
XP/sinX = YP/sinY = 34/sinZ
draw a line from x to y
To calculate the distance of the flag pole from points x and y, we can use trigonometry and the given bearings.
Step 1: Draw a diagram
Draw a diagram representing the situation described. Place point y at the origin (0,0) and point x to the right of y, 34m due east. Draw a line from x towards the north-east at an angle of 40 degrees. Also, draw a line from x towards the north-west at an angle of 18 degrees. The flag pole will be located at the intersection of these two lines.
Step 2: Determine the coordinates of point x
Given that point x is 34m due east of point y, the coordinates of x can be written as (34,0).
Step 3: Convert bearings to angles
The bearing N 18 W means the line is oriented 18 degrees west of due north (or towards the south-west). The bearing N 40 E means the line is oriented 40 degrees east of due north (or towards the north-east).
Step 4: Calculate the coordinates of the flag pole
To find the coordinates of the flag pole, we need to determine how far the two lines need to be extended from point x in order to intersect. We can use the tangent function to calculate these distances.
First, calculate the distance of the flag pole towards the north-east:
DistanceNE = 34m * tan(40 degrees)
Next, calculate the distance of the flag pole towards the north-west:
DistanceNW = 34m * tan(18 degrees)
Step 5: Calculate the distance between the flag pole and each point
To find the distance between the flag pole and point x, we can use the Pythagorean theorem. We know the coordinates of point x (34,0) and the coordinates of the flag pole, so we can calculate the distance between them.
DistanceXFlagPole = √((x2 - x1)^2 + (y2 - y1)^2)
DistanceXFlagPole = √((34 - DistanceNW)^2 + DistanceNE^2)
To find the distance between the flag pole and point y, we need to subtract the coordinates of point y (0,0) from the coordinates of the flag pole:
DistanceYFlagPole = √(FlagPole_X^2 + FlagPole_Y^2)
Step 6: Substitute values and calculate distances
Now, substitute the values obtained in the previous steps into the formulas and calculate the distances:
DistanceNE = 34m * tan(40 degrees)
DistanceNW = 34m * tan(18 degrees)
DistanceXFlagPole = √((34 - DistanceNW)^2 + DistanceNE^2)
DistanceYFlagPole = √(FlagPole_X^2 + FlagPole_Y^2)
By substituting these values and performing the calculations, you can find the distance of the flag pole from points x and y.
To calculate the distance of the flagpole from points x and y, we can use trigonometry and the given information about bearings.
First, let's draw a diagram to visualize the problem. Place points x and y on a coordinate plane, with x 34m due east of y.
```
Y (0,0)
|
|
|
|
---------X (34,0)
```
Next, let's identify the bearings to determine the direction from each point to the flagpole.
- The bearing from point x to the flagpole is N 18 W, which means it is 18 degrees west of north.
- The bearing from point y to the flagpole is N 40 E, which means it is 40 degrees east of north.
Now, we can calculate the distance of the flagpole from point x and point y by breaking it down into a x (horizontal) and y (vertical) components using trigonometry.
Let's first find the distance from point x to the flagpole. Since the bearing is given in a direction that is 18 degrees west of north, we need to convert it into a value relative to the x-axis.
To do this, we can use the concept of bearing angles as follows:
- The bearing from x is 18 degrees west of north, so the angle relative to the x-axis is 90 degrees - 18 degrees = 72 degrees.
- The distance from x to the flagpole is represented by the horizontal component, which is adjacent to the angle 72 degrees.
Using trigonometry, we can calculate the horizontal component:
horizontal component = distance from x to the flagpole * cos(72 degrees)
To find the vertical component, we can use the same concept:
- The bearing from y is 40 degrees east of north, so the angle relative to the x-axis is 90 degrees + 40 degrees = 130 degrees.
- The distance from y to the flagpole is represented by the vertical component, which is adjacent to the angle 130 degrees.
Using trigonometry, we can calculate the vertical component:
vertical component = distance from y to the flagpole * cos(130 degrees)
Finally, we can use the Pythagorean theorem to calculate the distance from point x or point y to the flagpole:
distance from x or y to the flagpole = √(horizontal component)^2 + (vertical component)^2
By substituting the values of the given bearings and distance from point x to point y, we can calculate the distance from point x and point y to the flagpole.