1. We'll start with a common Grade 10 trigonometry problem: Find the value of angle $\theta$ given $\sin \theta = 0.6$. 2. To find $\theta$, we use the inverse sine function: $$\theta = \sin^{-1}(0.6)$$. 3. Using a calculator, $\sin^{-1}(0.6) \approx 36.87^\circ$. 4. Therefore, $\theta \approx 36.87^\circ$. 5. If the problem specifies radians, convert degrees to radians using: $$\theta_{rad} = \theta_{deg} \times \frac{\pi}{180}$$. 6. For exploration, suppose we want to find the lengths of sides in a right triangle where the hypotenuse is 10 units and the angle $\theta = 36.87^\circ$. 7. Opposite side length: $$\text{opposite} = 10 \times \sin(36.87^\circ) = 10 \times 0.6 = 6$$. 8. Adjacent side length: $$\text{adjacent} = 10 \times \cos(36.87^\circ) \approx 10 \times 0.8 = 8$$. In summary, given $\sin \theta = 0.6$, $\theta \approx 36.87^\circ$, opposite side = 6 units, and adjacent side = 8 units when hypotenuse = 10 units.