Target Mathematics

1.70: Areas using trigonometry

4PM1/1/January/2017 — Question 5 · 11 marks

1.70 diagram 1
Figure 2 shows the quadrilateral ABCDABCD in which AB=BCAB=BC.
DC=8 cmAC=12 cm∠ABC=120∘∠CAD=35∘DC=8\text{ cm}\qquad AC=12\text{ cm}\qquad \angle ABC=120^\circ\qquad \angle CAD=35^\circ
Find
(a) the exact length, in cm, of ABAB. (2)
Given that angle ADCADC is obtuse, find
(b) the size, in degrees to 1 decimal place, of angle ADCADC, (3)
(c) the area, in cm2\text{cm}^2 to 3 significant figures, of the quadrilateral ABCDABCD. (6)