C2 June 2013 (R) Q8

EdexcelOld spec10 marksRadians

8.

Figure 2: triangle ABC with AB = 7 m, AC = 13 m, BC = 10 m and angle theta rad at A; arc BD of a circle centre A with D on AC, and the shaded region S between the arc BD and the lines BC and DC
Figure 2

Figure 2 shows the design for a triangular garden \(ABC\) where \(AB = 7\) m, \(AC = 13\) m and \(BC = 10\) m.

Given that angle \(BAC = \theta\) radians,

(a) show that, to 3 decimal places, \(\theta = 0.865\) (3)

The point \(D\) lies on \(AC\) such that \(BD\) is an arc of the circle centre \(A\), radius 7 m.

The shaded region \(S\) is bounded by the arc \(BD\) and the lines \(BC\) and \(DC\). The shaded region \(S\) will be sown with grass seed, to make a lawned area.

Given that 50 g of grass seed are needed for each square metre of lawn,

(b) find the amount of grass seed needed, giving your answer to the nearest 10 g. (7)
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