A freighter leaves on a course of 120 degrees and travels 515 miles. The ship then turns and goes due east 200 miles. What is the bearing and distance from the port to the ship?
I calculated 142 miles for distance but couldn't get bearing. Any help is appreciated.
Since i already ansvered your planes i might do this aswell.
General advice for all these, if you don't know what to do instantly draw a picture.
Same cosine therom as in other one.
Draw a picture into a triangle, have the starting point as origo and draw coordinate system there, you'll need an extra triangle to work out the angle between the cathetus. (hint: all angles of a triangle make 180 degrees and straight angle is 180 degrees aswell)
Distance is 695,4324... miles.
Bearing is already bit tougher but once you know the distance use sine function to figure out the angle opposite of the 200 mile side. Then 120-that angle gives you the ansver.
Bearing is 111,73246 degrees.
So that's 695,4354 miles and 111,73246 degrees or 695.4324 miles and 111.73246 just making sure seemed like a lot
well i'm from Finland we use commas to show where decimals start. So the ansver is 695 miles and a bit more. It's dot in USA to show where decimals begin?
To calculate the bearing and distance from the port to the ship, we can use vector addition.
First, let's break down the movements of the freighter.
According to the information given, the freighter initially travels on a course of 120 degrees for 515 miles. This can be represented as a vector. Let's call this vector A.
Next, the ship turns and goes due east for 200 miles. This can be represented as a vector. Let's call this vector B.
To find the resulting vector, we can add these two vectors together.
To add vectors A and B, we can use the head-to-tail method. We place the tail of vector B at the head of vector A, and draw a straight line from the tail of vector A to the head of vector B.
The vector that starts from the tail of vector A and ends at the head of vector B represents the resulting vector. Let's call this vector R.
To find the magnitude of vector R, we can use the Pythagorean theorem.
Magnitude of R = sqrt((Magnitude of A)^2 + (Magnitude of B)^2)
Magnitude of A = 515 miles
Magnitude of B = 200 miles
Magnitude of R = sqrt((515^2) + (200^2)) = sqrt(265225 + 40000) = sqrt(305225) = 553 miles (approximately)
Now, to find the bearing, we can use the inverse tangent function.
Bearing = arctan(Magnitude of B / Magnitude of A)
Bearing = arctan(200 / 515) = arctan(0.3883) = 21.41 degrees (approximately)
Therefore, the bearing and distance from the port to the ship are approximately 21.41 degrees and 553 miles, respectively.