Question 7

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)

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