A landscape artist plans to plant flowers within two concentric circles around a vertical light pole PQ. R is a point on the inner circle and S is a point on the outer circle. R, Q and S lie in the same horizontal plane. RS is a pipe used for the irrigation system in the garden.
- The radius of the inner circle is r units and the radius of the outer circle is QS.
- The angle of elevation from S to P is 30°.
- RQS = 2x and PQ =
7.1 Show that QS = 3r (3)
7.2 Determine, in terms of r, the area of the flower garden. (2)
7.3 Show that RS =:
7.4 If r = 10 metres and x = 56°, calculate RS. (2)