a ship leaves a port p and sail 30km due south. it then sail due west until it reaches a location H which is 60km from the port.what is the bearing of H and P?
As always, draw a diagram!
recall that the sides of a 30-60-90 degree right triangle are 1:√3:2
So, your have a triangle with sides 30, 30√3, and 60
If the ship turned west at point T, then
angle THP = 30°
I expect you can figure the required bearings now, eh?
To determine the bearings of location H and port P, we can use the concept of compass bearings.
Step 1: Identify the triangle formed by port P, location H, and the final position of the ship.
Step 2: Determine the components of the triangle:
- The ship traveled 30 km due south from port P.
- The ship traveled 60 km due west from the end of the southern journey to reach location H.
Step 3: Draw a diagram with the given information:
|
|
30 km | H
|___________
| P
|
Step 4: Using the triangle formed, we can find the bearing of H from P:
- Since H is west of P, the bearing can be described as "W (x°) N."
Step 5: Find the bearing of P from H:
- Since P is east of H, the bearing can be described as "E (x°) S."
Please note that the specific angles (x°) need to be measured from a reference point (usually north).
To determine the bearing of H and P, we need to find the angle between the line connecting P and H and the north direction.
Step 1: Draw a diagram representing the situation.
- Mark a point for the port P.
- Draw a line segment representing the ship's path to the south, 30km long.
- Mark the endpoint of the line segment as S.
- Draw a line segment from point S to point H, representing the ship's path westward, 60km long.
- Label the angle between the line from P to H and the north direction as θ (theta).
Step 2: Determine the direction and distance of the ship's path from P to W.
- Since the ship sails 30km due south from port P, the direction is 180 degrees or due south.
- The ship's distance from P to S is 30km.
Step 3: Determine the direction and distance of the ship's path from S to H.
- As the ship sails westward, the direction is 270 degrees or due west.
- The ship's distance from S to H is 60km.
Step 4: Calculate the bearing of H from P.
- Sum the angles to find the bearing of H from P.
- Since the ship first sailed south (180 degrees) and then west (270 degrees), the bearing of H from P is the sum of 180 and 270 degrees.
- 180 + 270 = 450 degrees.
Therefore, the bearing of H from P is 450 degrees.