A boat sails 40km from point A to point B, east of A on a lake. Lodge P is south of point A. Another lodge Q is south of point B. The bearing of Q from point A is S52degresE and the bearing of P from B is S39degresW.
If P is 60km from Q, calculate the bearing of lodge Q from lodge P.
Help me understand this question.
tan(90-39) = AP/40
so
AP = 49.4
tan (90-52) = BQ/40
so
BQ = 31.2
so
P is (49.4-31.2) or 18.1 km south of Q and 40 km west of q
tan theta = 40/18.1
theta = 65.7 degrees east of north from P to Q
The question asks for the bearing of lodge Q from lodge P.
To understand the question better, let's break down the given information:
- A boat sails 40km from point A to point B, which means point B is located 40km east of point A on a lake.
- Lodge P is south of point A. This means that lodge P is located somewhere to the south of point A.
- Lodge Q is south of point B. This means that lodge Q is located somewhere to the south of point B.
- The bearing of lodge Q from point A is given as S52 degrees E. This means that when you face north at point A, lodge Q is located 52 degrees to the south and slightly to the east.
- The bearing of lodge P from point B is given as S39 degrees W. This means that when you face north at point B, lodge P is located 39 degrees to the south and slightly to the west.
- It is also mentioned that lodge P is 60km from lodge Q.
Now, based on this information, we need to calculate the bearing of lodge Q from lodge P.
Sure! Let's break down the question and the given information:
1. Boat Sailing: The boat sails 40 km from point A to point B, east of A on a lake. This implies that point B is located to the east of point A.
2. Lodges: There are two lodges mentioned - Lodge P and Lodge Q. The question mentions that Lodge P is south of point A, and Lodge Q is south of point B.
3. Bearings: Bearings are angles measured clockwise from the north direction. The bearing of Q from point A is given as S52 degrees E, which means that the angle between the north direction and the line connecting point A to Q is 52 degrees east of south. Similarly, the bearing of P from B is given as S39 degrees W, which means the angle between the north direction and the line connecting point B to P is 39 degrees west of south.
4. Distance: The distance between Lodge P and Lodge Q is mentioned as 60 km.
Based on this information, we need to calculate the bearing of Lodge Q from Lodge P.
Now, let's understand how to calculate the bearing:
1. Draw a diagram: Draw a diagram to represent the situation described. Place point A and point B, and draw a line segment connecting them. Label this line segment as AB, representing the boat's path. Place Lodge P below point A and Lodge Q below point B.
2. Calculate the angles: To determine the bearing of Lodge Q from Lodge P, we need to find the angle between the line segment joining Lodge P to Lodge Q and the reference direction (north).
To do this, we can add the angle between the line segment PB and the north direction (S39 degrees W) to the angle between the line segment BQ and the north direction (S52 degrees E).
3. Calculate the final bearing: Once we obtain the combined angle, we can use it to determine the bearing. Subtract the result from 180 degrees to get the final bearing, keeping in mind that the bearing is always measured clockwise from the north direction.
I hope this helps in understanding the question and the approach to solve it.