Math CentralQuandaries & Queries


Question from vinton, a student:

ok there is a triangle labeled q, p, r......the three towns p, q, r are such that the bearing of p from q is 070 degrees.
r is 10 km due east of q and pq = 5km.

(i) calculate correct to one decimal place, the distance of pr.
(ii) given that angle qpr 142 degrees, state the bearing of r from p


If the bearing is measured counterclockwise from north then I have this diagram (all the distances are in kilometers).


s is the point where the north-south line meets the line joining p and r. I let the distance from p to s be x km and the distance from q to s be y km. You can use the sine and cosine of 70o to find x and y. Since triangle rsq is a right triangle you can use Pythagoras theorem to find the distance from p to q.


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