1.31: Past-paper question 3

4PM1/1R/June/2024 — Question 3 · 8 marks

1.31 diagram 1
Figure 1 shows triangle ABC\displaystyle ABC where
AB=xcmAC=(x+7)cm∠BAC=30∘AB = x \mathrm{cm} \quad AC = (x + 7) \mathrm{cm} \quad \angle BAC = 30^\circ
The area of triangle ABC=36cm2\displaystyle ABC = 36 \mathrm{cm}^2
(a) Show that x=9\displaystyle x = 9
(3)
(b) Find, in cm to 3 significant figures, the length of BC\displaystyle BC
(2)
(c) Find, in degrees to one decimal place, the size of
(i) ∠ABC\displaystyle \angle ABC
(ii) ∠ACB\displaystyle \angle ACB
(3)