'A ship sales for 60km on bearing 040 degrees.How far east of it is the starting point?'
From a point p, town A is 20km away ona bearing of 040degree and town B is 30km away a bearing 126degree. find distance of B from A
Why did the ship sail in the first place? Did it want to find some pirate treasure or maybe meet some friendly dolphins? Regardless, let's do some math to figure out how far east the starting point is from the ship's current position. So, if the ship sailed 60 km on a bearing of 040 degrees, it means it went 60 km in the northeast direction. To find out how far east it is from the starting point, we'll need to use some trigonometry. Let me just get my trusty calculator... Ah, here it is! Alright, so using my advanced mathematical skills, the ship is roughly 46.7 km east of its starting point. See, math can be fun! Just like sailing with pirates and dolphins.
To find the distance east of the starting point, we need to use trigonometry and the concept of bearings.
In this scenario, the ship travels on a bearing of 040 degrees. Bearing is the direction in which an object is moving or facing, measured in degrees clockwise from true north.
Step 1: Understanding the bearing
- In this case, bearing 040 degrees means the ship is moving 40 degrees clockwise from true north.
- The angle formed by the starting point, the ship's current position, and the destination point is 40 degrees.
- This angle can be visualized using a compass rose, where north is at the top (0 degrees), and we move clockwise.
Step 2: Applying trigonometry
- We know the ship traveled 60 km. Let's assume the direction is directly north and south.
Step 3: Breaking down the problem
- The ship moves east and north, forming a right-angled triangle.
- The distance east of the starting point is the adjacent side of the angle formed.
- We need to find the length of this adjacent side.
Step 4: Calculating the distance east
- Since we have the hypotenuse (60 km) and we want to find the adjacent side, we can use the trigonometric function cosine (cos).
- The cosine of an angle is equal to the adjacent side divided by the hypotenuse.
- Therefore, we can use the formula: adjacent side = hypotenuse * cos(angle).
Step 5: Applying the formula
- In this case, the angle is 40 degrees, and the hypotenuse is 60 km.
- Plug in the values: adjacent side = 60 km * cos(40°).
Step 6: Calculating the cosine
- To calculate cosine (cos) using a calculator or programming language, make sure it's in degree mode.
- Enter 40 and find the cosine value: cos(40°) ≈ 0.7660.
Step 7: Applying the cosine value
- Plug the cosine value into the formula: adjacent side = 60 km * 0.7660.
- Calculate the result: adjacent side ≈ 45.96 km.
Therefore, the ship is approximately 45.96 km east of its starting point.
60sin(40°)
The ship is east of the starting point. Your question is worded backwards.