A traveler moves from town p on a bearing of 055 degrees to another town q 200km away he then moves from q on a bearing of 155 degrees to another town r 400km from q.find the distance between p and r
draw a diagram, and then use the law of cosines.
To find the distance between town p and town r, we can use the concept of vectors and the "law of cosines."
Step 1: Determine the position of town r relative to town q.
Since the traveler moves from town q on a bearing of 155 degrees to another town r, we can draw a vector from town q to town r, using the given distance of 400km and the bearing angle.
Step 2: Determine the position of town q relative to town p.
Since the traveler moves from town p on a bearing of 055 degrees to town q, we can draw a vector from town p to town q, using the given distance of 200km and the bearing angle.
Step 3: Determine the resultant vector from town p to town r.
To find the resultant vector from town p to town r, we can add the vectors obtained in steps 1 and 2. This can be done by breaking down the vectors into their x and y components (north-south and east-west).
Step 4: Apply the law of cosines to find the distance between p and r.
Using the resultant vector obtained in step 3, we can determine the magnitude (length) of the vector, which represents the distance between town p and town r. This can be done using the law of cosines, which states that:
c^2 = a^2 + b^2 - 2ab * cos(C)
where c is the side opposite the angle C, and a and b are the lengths of the other two sides.
By substituting the values of a, b, and C from the resultant vector, we can calculate c, which represents the distance between p and r.