1. The problem states that $\sin \theta = \frac{1.5}{9.4}$. We need to find the angle $\theta$ to 1 decimal place. 2. Recall that $\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}$. To find $\theta$, use the inverse sine function: $$\theta = \sin^{-1}\left(\frac{1.5}{9.4}\right)$$ 3. Calculate the fraction: $$\frac{1.5}{9.4} \approx 0.1596$$ 4. Find the inverse sine: $$\theta = \sin^{-1}(0.1596) \approx 9.2^\circ$$ 5. So, $\theta$ is approximately $9.2$ degrees to 1 decimal place. --- For the second part: a) Write an expression for $\sin \theta$ in terms of $x$. 1. Given a right-angled triangle with hypotenuse 10 cm and side opposite $\theta$ labeled $x$, by definition: $$\sin \theta = \frac{x}{10}$$ b) If $\sin \theta = \frac{3}{5}$, find $x$. 1. Use the expression from part (a): $$\frac{3}{5} = \frac{x}{10}$$ 2. Cross-multiply to solve for $x$: $$x = 10 \times \frac{3}{5} = 6$$ 3. So, the length $x$ is 6 cm.