1. **State the problem:** We have a right-angled triangle with side lengths 3 cm (vertical), 7 cm (horizontal), and an unknown hypotenuse. Angle $\theta$ is located at the bottom-right corner, adjacent to the horizontal side of length 7 cm. We need to determine which equation (A, B, or C) relating $\sin \theta$, $\cos \theta$, and $\tan \theta$ is correct. 2. **Analyze the triangle:** Given the right angle at the bottom-left corner, the triangle's sides are: - Opposite side to $\theta$: vertical side = 3 cm - Adjacent side to $\theta$: horizontal side = 7 cm - Hypotenuse: Calculate using Pythagoras: $$\text{hypotenuse} = \sqrt{3^2 + 7^2} = \sqrt{9 + 49} = \sqrt{58}$$ 3. **Check each equation:** - Equation A: $\sin \theta = \frac{3}{7}$ The sine of $\theta$ is the ratio of opposite side over hypotenuse: $$\sin \theta = \frac{3}{\sqrt{58}} \approx 0.394$$ However, $\frac{3}{7} \approx 0.429$, so A is **not correct**. - Equation B: $\cos \theta = \frac{3}{7}$ The cosine of $\theta$ is adjacent over hypotenuse: $$\cos \theta = \frac{7}{\sqrt{58}} \approx 0.918$$ $\frac{3}{7} \approx 0.429$, so B is **not correct**. - Equation C: $\tan \theta = \frac{3}{7}$ The tangent of $\theta$ is opposite over adjacent: $$\tan \theta = \frac{3}{7} \approx 0.429$$ This matches equation C exactly, so C is **correct**. 4. **Find angle $\theta$ in degrees:** Use the tangent inverse function: $$\theta = \tan^{-1}\left(\frac{3}{7}\right)$$ Calculate: $$\theta \approx \tan^{-1}(0.4286) \approx 23.2^\circ$$ Rounded to 1 decimal place, $\theta = 23.2^\circ$. **Final answers:** - a) Equation C is correct: $\tan \theta = \frac{3}{7}$. - b) Angle $\theta = 23.2^\circ$ to 1 decimal place.