1.21: Past-paper question 3

4PM1/1R/June/2023 — Question 3 · 9 marks

1.21 diagram 1
Figure 2 shows triangle ABC\displaystyle ABC where
AB=10cm,AC=8cm,BC=xcmand∠BAC=100∘AB = 10 \mathrm{cm}, \quad AC = 8 \mathrm{cm}, \quad BC = x \mathrm{cm} \quad \mathrm{and} \quad \angle BAC = 100^\circ
(a) Find, to 3 significant figures, the value of x\displaystyle x
(2)
(b) Find, in degrees to one decimal place, the size of
(i) angle ABC\displaystyle ABC
(3)
(ii) angle ACB\displaystyle ACB
The bisector of angle ABC\displaystyle ABC meets AC\displaystyle AC at the point M\displaystyle M
(c) Find the area, in cm2\displaystyle \mathrm{cm}^2 to 3 significant figures, of triangle BMC\displaystyle BMC.
(4)