SOLUTION: Two surveyors are on the opposite sides of a swamp. To find the distance between them, one surveyor locates a point T that is 180 m to point P, her location. The other surveyor loc

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Question 43163: Two surveyors are on the opposite sides of a swamp. To find the distance between them, one surveyor locates a point T that is 180 m to point P, her location. The other surveyor locates point R, which is 80 m from point T and creates an angle of 72o for angle PTR. Find the distance across the swamp (PR).
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
This problem is very if you draw the figure first.
Consider the triangle PTR.
Let p, t and r be the lengths of the sides RT, PR and PT respectively.
Also, denote the internal abgles of the triangle as P, T and R e.g. < RTP = T.



Look, you know from the given data that r = 180 m, p = 80 m and T = 72%5Eo.
Now you are required to find 't'.
In order to find 't' apply cosine rule.
t%5E2+=+p%5E2+%2B+r%5E2+-+2%2Ap%2Ar%2Acos%28T%29
or t%5E2+=+80%5E2+%2B+180%5E2+-+2%2A80%2A180%2Acos%2872%5Eo%29
or t%5E2+=+6400+%2B+32400+-+28800cos%2872%5Eo%29
or t%5E2+=+38800+-+28800%2A0.309
or t%5E2+=+38800+-+8899.7
or t%5E2+=+29900.3
or t+=+sqrt%2829900.3%29
or t+=+172.92

Hence, the required length of PR is 172.92 m.