P;Q AND R ARE VILLAGERS ON A LEVEL GROUND. Q IS 4KM ON A BEARING OF O40 FROM P,WHILE R IS 3KM ON THE BEARING OF 130 FROM Q.CALCULATE THE DISTANCE AND BEARING OF 2 FROM P
First do not use all caps.
Second, it would help if you would proofread your work before you post it.
What is "2"?
To calculate the distance and bearing of point 2 from point P, we need to break down the steps.
Step 1: Determine the coordinates of point P.
Since P is on a level ground, we can assume it to be the origin (0,0).
Step 2: Calculate the coordinates of point Q.
Given that Q is 4km on a bearing of 040 from P, we can use trigonometry to calculate its coordinates. The bearing of 040 corresponds to an angle of 40 degrees measured clockwise from the positive x-axis.
Using the formula:
x = distance x cos(angle)
y = distance x sin(angle)
Let's calculate the coordinates of Q:
x = 4km x cos(40°)
y = 4km x sin(40°)
Step 3: Calculate the coordinates of point R.
Given that R is 3km on a bearing of 130 from Q, we can again use trigonometry to calculate its coordinates. The bearing of 130 corresponds to an angle of 130 degrees measured clockwise from the positive x-axis.
Using the same formula as above, we can calculate the coordinates of R relative to Q:
x = 3km x cos(130°)
y = 3km x sin(130°)
Step 4: Calculate the combined coordinates of point 2.
To calculate the coordinates of point 2 from P, we need to add the coordinates of R to Q:
x2 = xQ + xR
y2 = yQ + yR
Step 5: Calculate the distance between point P and point 2.
The distance between two points can be calculated using the distance formula:
distance = sqrt((x2 - xP)^2 + (y2 - yP)^2)
Step 6: Calculate the bearing from P to 2.
The bearing can be calculated using trigonometry. The angle can be determined using the atan2 function:
angle = atan2(y2 - yP, x2 - xP)
bearing = (angle + 360) % 360
Let's plug in the values and calculate the distance and bearing to point 2.