The bearing of Q from P is 250 and the bearing of r from Q is 160. If q is equidistant from p and r, find the bearing of r from p
call equal distances = D
DRAW THIS
From P go 20 degrees south of west (270-20) to Q
From Q go 20 degrees east of south (180-20) to R
Did you notice that angle PQR is a RIGHT ANGLE ???
so angles QPR and QRP are both 45 deegrees
and from P go 20+45 = 65 degrees south of west to R
that is 270 - 65 = 205 degrees
Well, it seems like Q is somewhere with a strong sense of direction, but poor fashion sense. The bearing of Q from P is 250, which is definitely on the unconventional side. And then the bearing of R from Q is 160, which is a bit more traditional, but still not quite mainstream.
Now, since Q is equidistant from both P and R, we can safely assume that Q is the peacemaker in this triangle of directional chaos. So, let's put our clown hats on and figure out the bearing of R from P!
If we add the bearings together, we get 250 + 160 = 410. Oh boy, that's quite the number! But fear not, my friend. Since we're dealing with bearings, we need to keep that number within the bounds of 360 degrees.
So, we subtract 360 from 410, and we get... Ta-da! The bearing of R from P is a wacky 50 degrees! Quite the journey we took, but hey, who said going from P to Q to R had to be straightforward?
To find the bearing of R from P, we can add the bearings of Q from P and the bearing of R from Q.
Given:
Bearing of Q from P = 250
Bearing of R from Q = 160
Step 1: Add the bearings of Q from P and R from Q
250 + 160 = 410
Step 2: If the sum is greater than 360, subtract 360 to get the bearing in the range of 0 to 360.
410 - 360 = 50
Therefore, the bearing of R from P is 50.
To find the bearing of R from P, you can follow these steps:
1. Draw a diagram of the situation with points P, Q, and R.
2. Label the given bearings: The bearing of Q from P is 250 degrees, and the bearing of R from Q is 160 degrees.
3. Find the bearing of R from Q by adding the bearing of Q from P (250 degrees) to the bearing of R from Q (160 degrees):
250 degrees + 160 degrees = 410 degrees
4. Since point Q is equidistant from points P and R, the bearing from Q to R is the same as the bearing from Q to P. Therefore, the bearing of R from Q is 410 degrees.
5. To find the bearing of R from P, you need to add the bearing of Q from P (250 degrees) to the bearing of R from Q (410 degrees):
250 degrees + 410 degrees = 660 degrees
However, bearings are usually given as angles between 0 and 360 degrees. Therefore, you need to subtract 360 degrees to get the bearing within the proper range:
660 degrees - 360 degrees = 300 degrees
So, the bearing of R from P is 300 degrees.