1.59: Sine Rule and Triangle Area

4PM1/1R/June/2019 — Question 2 · 6 marks

1.59 diagram 1
Figure 2 shows triangle ABC\displaystyle ABC in which
AB=2x cm,AC=3x cm,BC=4x cm.AB=2x\text{ cm}, \qquad AC=3x\text{ cm}, \qquad BC=4x\text{ cm}.
(a) Show that
sin⁡ABC=31516.\sin ABC=\frac{3\sqrt{15}}{16}.
(4)
Given that the area of triangle ABC\displaystyle ABC is
751564 cm2,\frac{75\sqrt{15}}{64}\text{ cm}^2,
(b) find the value of x\displaystyle x.
(2)