two ships p and q left a
port at the same time. q sailed on a
bearing of 150 while p sailed on the
north side of q. after a distance of
8km and 10km by pand q
respectively, their distance apart
was 12km. find the bearing of p
and r
067degree
067.2
show me the steps and the working
To find the bearing of ship P and Q, we can use trigonometry and the concept of bearings.
Let's start by drawing a diagram to visualize the situation:
P
|\
| \
| \
| \
| \
| \ Q
| \
12 km
Ship P is on the north side of Ship Q, that means they sailed in different directions.
Let's assume the starting point as Point O, and the position of Ship P as Point A, and the position of Ship Q as Point B.
Now, we have a right-angled triangle with sides of lengths 8 km, 10 km, and 12 km.
From the given information, we can deduce that the triangle formed is a 3-4-5 right-angled triangle.
Using the concept of trigonometry, we can find the angles and bearings.
In triangle OAB, the angle at Point A can be found using the cosine formula:
cos(A) = adjacent / hypotenuse
cos(A) = 8 km / 12 km
cos(A) = 2/3
A = arccos(2/3)
Now, we can find the bearing of Ship P using the bearing notation.
Bearing is typically measured in degrees clockwise from the north.
Since Ship Q sailed on a bearing of 150 degrees, the bearing of Ship P will be 150 + A degrees.
Bearing of Ship P = 150 + A
Simplify the expression to find the bearing of Ship P.
who is r?
If x is the angle between p and q, then
12^2 = 8^2+10^2-160cos(x)
Now subtract x from q's heading (not bearing!)