P,Q and R are points on the same horizontal plane. The bearing of Q from P is 150 and the bearing of R from Q is 060. if PQ=5 and QR=3, find the bearing of R from P, correct to the nearest degree.
check out "kelvin" 's post at
https://www.jiskha.com/questions/1515062/P-Q-and-R-are-points-on-the-same-horizontal-plane-the-bearing-of-Q-from-P-is-150
All angles are measured CW from +y-axis,
PR = PQ + QR = 5[150o] + 3[60o],
X = 5*sin150 + 3*sin60 = 5.1,
Y = 5*Cos150 + 3*Cos60 = -2.83,
TanA = X/Y,
A = -61o = 61o E. of S. = 119o CW.
So the bearing of R from P = 119o.
To find the bearing of point R from point P, we can use the concept of bearings and trigonometry.
Step 1: Draw a diagram:
- Mark point P, Q, and R on a horizontal plane.
- Label the angle between PQ and the reference direction as A.
- Label the angle between QR and the reference direction as B.
Step 2: Calculate the angle between PQ and QR:
- Since angle QPR is a straight angle (180°), we can calculate it by subtracting angle PQ from angle QR.
- Angle QPR = Angle QR - Angle PQ = 060° - 150° = -90°.
Step 3: Adjust the negative angle:
- Since the bearing should be between 0° and 360°, we need to adjust the negative angle.
- Add 360° to the negative angle to obtain the positive angle.
- Angle QPR = -90° + 360° = 270°.
Therefore, the bearing of point R from point P is 270°, correct to the nearest degree.
To find the bearing of point R from point P, we can use the concept of bearings and trigonometry. Here's how you can solve the problem:
Step 1: Understand the problem:
- The bearings represent the angle between a reference direction (usually North) and the line connecting two points on a plane.
- A bearing is measured clockwise from the reference direction.
- The problem states that P, Q, and R are on the same horizontal plane, and their relationships and distances are given.
- We need to find the bearing of R from P.
Step 2: Determine the bearings:
- The bearing of Q from P is 150 degrees.
- The bearing of R from Q is 60 degrees.
Step 3: Visualize the situation:
- Draw a horizontal plane and mark points P, Q, and R.
- Label the given distances: PQ = 5 and QR = 3.
Step 4: Find the bearing of R from P:
- To find the bearing of R from P, we need to calculate the angle formed by the line PR and the reference direction.
- Since the reference direction is not provided, we can assume it's North.
- Using the given bearings, we can calculate the angle QPR, and then subtract it from 360 degrees to find the bearing of R from the reference direction (North).
- Let's calculate the angle QPR:
- QPR = 180 degrees (bearing of Q from P) + 60 degrees (bearing of R from Q)
- QPR = 240 degrees.
- Now, subtract the angle QPR from 360 degrees to find the bearing from the reference direction:
- Bearing of R from reference direction = 360 degrees - QPR = 360 degrees - 240 degrees = 120 degrees.
Step 5: Final answer:
- The bearing of R from P, correct to the nearest degree, is 120 degrees.