Two Ship A And B Value A Part The Same Time.A Travel On A Bearing Of 159 And B Travel On A Bearing Of 215 After Some Time A Is 9KM From P And The Bearing Of B From A Is 256.Calculate The Distance Of B From P
You garbled phrasing " Value A Part The Same Time" makes me work to understand what you are saying. I assume you meant "Two ships A and B depart from port P at the Same Time"
If you draw triangle PAB, you should be able to see that
∠P = 56°
∠A = 83°
∠B = 180-56-83 = 41°
So, using the law of sines,
PB/sin83° = 9/sin41°
PB = 13.6 km
Give me solution
To solve this problem, we can use the concept of triangulation. Let's break it down step by step:
Step 1: Draw a diagram
Draw a diagram with points A, B, and P as shown:
```
A
/ .
/ .
P ---- B
```
Step 2: Determine the angle at point A
Given that ship A is traveling on a bearing of 159 degrees, it means that angle APB is 159 degrees.
Step 3: Calculate the distance from A to B
Since we have the angle APB and the distance from A to P, we can use the Law of Cosines to find the distance from A to B:
AB^2 = AP^2 + BP^2 - 2 * AP * BP * cos(159)
Step 4: Calculate the bearing of B from P
Given that ship B is traveling on a bearing of 215 degrees and the bearing is measured from the north direction, we need to convert it to the bearing measured from the east direction:
Bearing of B from P = 90 - 215 = -125 degrees (measured from the east direction)
Step 5: Determine the angle at point P
Given that the bearing of B from P is -125 degrees, it means that angle PBA is 256 degrees (360 - 125).
Step 6: Apply the Law of Sines to find the distance of B from P
Using the Law of Sines, we can set up the following ratio:
BP / sin(256) = AB / sin(256 + 159)
Now, substitute the value of AB from Step 3 into the equation:
BP / sin(256) = sqrt (AP^2 + BP^2 - 2 * AP * BP * cos(159)) / sin(415)
Now you can solve this equation to find the distance of B from P.
To calculate the distance of ship B from point P, we can use the concept of trigonometry and the given information about the bearings and distances.
Let's break down the given information step-by-step:
1. Ship A travels on a bearing of 159° from the starting point.
2. Ship B travels on a bearing of 215° from the starting point.
3. After some time, ship A is 9 km from point P.
4. The bearing of ship B from ship A is 256°.
To solve the problem, we need to find the distance of ship B from point P.
Step 1: Draw a diagram
Draw a diagram with the starting point, point P, ship A, and ship B. Label the positions of ship A and point P.
Step 2: Determine the position of ship A relative to the starting point
Since ship A is 9 km from point P, mark a point on the line connecting the starting point and point P, 9 km away from the starting point. This point represents the position of ship A.
Step 3: Determine the position of ship B relative to ship A
Using the given bearing of 256°, draw a line from ship A in the direction of the bearing. This line represents the possible positions of ship B.
Step 4: Determine the possible position of ship B from point P
From the possible positions of ship B, find the point that is on the line connecting ship A and point P. This point represents the possible position of ship B relative to point P.
Step 5: Measure the distance between ship B and point P
Using a ruler or any measuring tool, measure the distance between the possible position of ship B and point P. This distance represents the distance of ship B from point P.
Now, you should have the distance of ship B from point P.