1. **Problem statement:** Find the length of the missing side in each right triangle given the angles and the right angle. 2. **Recall the trigonometric ratios:** For a right triangle with angle $\theta$, the sides relate as: - $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$ - $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$ - $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$ 3. **Part a) Given:** - Angle $47^\circ$ at the top-left vertex - Right angle at bottom-left vertex - Missing side is the bottom horizontal side (adjacent to $47^\circ$) Assuming the hypotenuse length is 1 (unit triangle) for calculation: Using cosine to find adjacent side: $$\cos(47^\circ) = \frac{\text{adjacent}}{1} = \text{adjacent}$$ Calculate: $$\text{adjacent} = \cos(47^\circ) \approx 0.681998$$ 4. **Part b) Given:** - Right angle at top-left vertex - Angle $21^\circ$ near the right vertex - Missing side is the left vertical side (opposite to $21^\circ$) Assuming hypotenuse length is 1: Using sine to find opposite side: $$\sin(21^\circ) = \frac{\text{opposite}}{1} = \text{opposite}$$ Calculate: $$\text{opposite} = \sin(21^\circ) \approx 0.358368$$ **Final answers:** - a) Missing side length $\approx 0.682$ - b) Missing side length $\approx 0.358$