maths _34

(a) h = psinθ + qcosθ
(b) (i)
Since p:q = 3:2 => p = 3q/2
Area = pq = (3q/2)q = 54
So 3q2 = 108
q2 = 36
q = 6 => p = 9
Perimeter = 2(6 + 9) = 30cm
(ii)
h = 9sinθ + 6cosθ = 3(3sinθ + 2cosθ)
Fromthe graph, when θ = 42, 3sinθ + 2cosθ = 3.5
So h = 3(3.5) = 10.5
(c)
Perimeter = 2(p + q) = 50
3q/2 + q = 25
5q/2 = 25
q = 10 => p = 15
h = 15sinθ + 10cosθ = 5(3sinθ + 2cosθ)
Since h = 14, so 3sinθ + 2cosθ = 14/5 = 2.8
From the graph θ = 17