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 The distance RT
To find the distance RT, we can use trigonometry.
First, let's draw a diagram to visualize the situation:
Q
|\
| \
40°| \
| \
| \
| \
R-----T
2.5km
From the diagram, we can see that the triangle PRT is a right triangle, with angle PRT being 90 degrees.
We can use the tangent function to find the height of the pole RT:
tan(40°) = RT / 2.5km
RT = 2.5km * tan(40°)
RT ≈ 2.19 km
Therefore, the distance RT is approximately 2.19 km.