SOLUTION: the location of 4 twins P,Q,R and T such that Q is on a bearing of 270 degrees from P. T is 12 km due to north of P and on a bearing of 47 degrees from Q. R is due north of Q a

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Question 1011905: the location of 4 twins P,Q,R and T such that Q is on a bearing of
270 degrees from P. T is 12 km due to north of P and on a bearing
of 47 degrees from Q. R is due north of Q and 16 km from P. Calculate
the distance between P and Q.

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
the location of 4 twins P,Q,R and T such that Q is on a bearing of
270 degrees from P. T is 12 km due to north of P and on a bearing
of 47 degrees from Q. R is due north of Q and 16 km from P. Calculate
the distance between P and Q.
Bearings when no direction is given are always taken 
rotating CLOCKWISE starting at NORTH (straight upward).
Due north means straight upward. [A bearing of 270° is
the same as 'due west', or "directly horizontal to
the left"]




This is not a very interesting problem because the 16 km given is not
even needed at all.  All we need is right triangle PQT, from which
we can find PQ.

We find that angle PQT is 90°-47° = 43° and so

tan%28PQT%29=PT%2F%28PQ%29

tan%28%2243%B0%22%29=12%2F%28PQ%29

PQ%2Atan%28%2243%B0%22%29=12

PQ=12%2Ftan%28%2243%B0%22%29

PQ=12%2F0.9325150861

PQ=matrix%281%2C2%2C11.19018103%2Ckm%29

It would be a lot more interesting problem if you had
been asked something that would require you to use the
16 km that was given, such as the distance from Q to R
or R to T.

Are you sure you copied the problem correctly?  If
so, the answer is 11.19 km, which does not involve the
16 km distance from.

If you did not copy the problem correctly and you were
asked for something else, then tell me what was asked
in the thank-you note form below, and I'll get back to
you by email.

Edwin