P and Q are two observation posts on the same horizontal ground asthe foot R of a vertical pole RT. P is 2.5km south of R. Q is east of R and is on a bearing of 065° from P. The angle of elevation of T from P is 40°.calculate, correct to three significant figures B. The distance RQ
To find the distance RQ, we can use trigonometry.
From the problem, we know that P is 2.5 km south of R. This means that the length of the line segment PR is 2.5 km.
We are also given that the angle of elevation of T from P is 40°. This means that angle PTR is 90° - 40° = 50°.
Since P is south of R, angle PRQ = angle PTR - 90° = 50° - 90° = -40°.
Therefore, angle PRQ = 180° + (-40°) = 140°.
Now we can use the Law of Sines to find the length of RQ.
sin(140°) / RQ = sin(65°) / PR
Using the given values, we can solve for RQ:
sin(140°) / RQ = sin(65°) / 2.5
RQ = (sin(65°) / 2.5) * (1 / sin(140°))
RQ ≈ 2.079 km
Therefore, the distance RQ is approximately 2.079 km.