An offshore oil well at point R is viewed from points P and Q, and <QPR and <RQP

Question

An offshore oil well at point R is viewed from points P and Q, and <QPR and <RQP are found to be 55°50 and 65°22', respectively. If points P and Q have coordinates (1487.7, 3452.8) and (3145.8, 5127.5), respectively, approximate the coordinates of R.

I calculated <PRQ as 58°48.
I calculated the distance from P to Q as 2356.6747.
I calculated the distance from P to R as 2504.4332.
I calculated the distance from Q to R as 2279.6489.
I believe the coordinates for R are (-1005.7, 16142.4).

I don't understand how these coordinates are calculated with the data I have. Any help would be appreciated.

Explanation / Answer

Step - 1: to find Angle R

Angle R = 180 deg - (angle P + angle Q)

Angle P = 55 deg+(50/60) deg = 55.833 deg

Angle Q = 65 deg+(22/60) deg = 65.366 deg

Angle R = 180 - (55.833+65.366)

= 58.801 deg = 58 deg 48 min

Step - 2: To find coordinates of R

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