A ship leaves a port and travels 21km on a bearing of 32 and then 45km on a bearing of 287 calculate its distance from the port and the bearing of the port from the ship
That's good
All angles are measured CW from +y-axis.
d = 21km[32o] + 45km[287o].
X = 21*sin32 + 45*sin287 = -31.91 km.
Y = 21*Cos32 + 45*Cos287 = 30.97 km.
d = -31.91 + 30.97i = 44.5km[-45.9o] = 44.5km[45.9o] W. of N. = 44.5km[314o] CW.
Tan A = X/Y.
give the diagram
The ship made a turn of 75 degrees when it changed course.
So, using the law of cosines, its distance d from port can be found via
d^2 = 21^2 + 45^2 - 2*21*45*cos75°
d = 44.5 km
The ship's final position is
28.97km W and 38.24km N of port
Now just turn that into a bearing - watch the direction you use -- from ship to port
Thanks but I need the diagram
OK
Sin 105 is cos -75
Please I Need The Diagram
Give working guide
I need the diagram of the above question
To solve this problem, we can use the concept of vectors and trigonometry.
First, let's represent the ship's movements as vectors. The first vector represents the ship's movement of 21 km on a bearing of 32°, and the second vector represents the ship's movement of 45 km on a bearing of 287°.
We can break down each vector into its horizontal (x) and vertical (y) components using trigonometry.
For the first vector:
The horizontal component (x1) is calculated using cos(32°) = adjacent / hypotenuse, where the adjacent side is x1.
So, x1 = cos(32°) * 21 km.
The vertical component (y1) is calculated using sin(32°) = opposite / hypotenuse, where the opposite side is y1.
So, y1 = sin(32°) * 21 km.
Similarly, for the second vector:
The horizontal component (x2) is calculated using cos(287°) = adjacent / hypotenuse, where the adjacent side is x2.
So, x2 = cos(287°) * 45 km.
The vertical component (y2) is calculated using sin(287°) = opposite / hypotenuse, where the opposite side is y2.
So, y2 = sin(287°) * 45 km.
Now, we can calculate the total horizontal (x) and vertical (y) displacement of the ship.
The total horizontal displacement (x) is the sum of x1 and x2.
The total vertical displacement (y) is the sum of y1 and y2.
x = x1 + x2
y = y1 + y2
Finally, we can use the Pythagorean theorem to find the distance from the port (d) and the bearing (θ) of the port from the ship.
d = √(x^2 + y^2)
θ = tan^(-1)(y / x)
Plugging in the values and evaluating the equations will give us the answer.
Note: The angles should be in radians when using trigonometric functions, so we need to convert the given angles from degrees to radians before using them in the trigonometric calculations.