8. $\triangle D E F$ has $\angle D=33^{\circ}, \angle F=75^{\circ}$, and $e=7.5 \mathrm{~m}$. Sketch the triangle. [2 marks]
Answer
\(\boxed{\text{In triangle DEF, angle D = 33°, angle E = 72°, angle F = 75°, side d ≈ 4.30 m, side e = 7.5 m, and side f ≈ 7.62 m}}\)
Step 1 ：Find the third angle: \(\angle E = 180 - \angle D - \angle F = 180 - 33 - 75 = 72^\circ\)
Step 2 ：Use the sine rule to find side d: \(\frac{d}{\sin{33^\circ}} = \frac{7.5}{\sin{75^\circ}} \Rightarrow d \approx 4.30 \mathrm{~m}\)
Step 3 ：Use the sine rule to find side f: \(\frac{f}{\sin{72^\circ}} = \frac{7.5}{\sin{75^\circ}} \Rightarrow f \approx 7.62 \mathrm{~m}\)
Step 4 ：\(\boxed{\text{In triangle DEF, angle D = 33°, angle E = 72°, angle F = 75°, side d ≈ 4.30 m, side e = 7.5 m, and side f ≈ 7.62 m}}\)
