Target Mathematics

1.90: Areas using trigonometry

4PM1/2/January/2015 — Question 1 · 7 marks

1.90 diagram 1
In triangle ABCABC, AB=xAB=x cm, AC=2xAC=2x cm and ∠ABC=100∘\angle ABC=100^\circ, as shown in Figure 1.
(a) Find, in degrees to the nearest 0.1∘0.1^\circ, the size of ∠BAC\angle BAC. (4)
Given that the area of triangle ABCABC is 16 cm216\text{ cm}^2,
(b) find, to 3 significant figures, the value of xx. (3)