Given a right triangle ABC with right angle at C, which of the following is the correct trigonometric ratio for $\angle A$?

• A. $\cos A=\frac{\mathrm{AC}}{\mathrm{AB}}$
• B. $\sin A=\frac{\mathrm{BC}}{\mathrm{AB}}$
• C. $\sin A=\frac{\mathrm{AC}}{\mathrm{BC}}$
• D. $\tan A=\frac{\mathrm{BC}}{\mathrm{AC}}$

Answer: (D)

Verified step by step guidance

1. Identify the sides of the right triangle relative to angle A. The side opposite angle A is BC, the side adjacent to angle A is AC, and the hypotenuse is AB.
2. Recall the definitions of the primary trigonometric ratios for an angle in a right triangle: - \(\sin A = \frac{\text{opposite}}{\text{hypotenuse}}\) - \(\cos A = \frac{\text{adjacent}}{\text{hypotenuse}}\) - \(\tan A = \frac{\text{opposite}}{\text{adjacent}}\)
3. Substitute the sides identified into these formulas: - \(\sin A = \frac{BC}{AB}\) - \(\cos A = \frac{AC}{AB}\) - \(\tan A = \frac{BC}{AC}\)
4. Compare the given options with these expressions to determine which matches the correct trigonometric ratio for angle A.
5. Conclude that the correct trigonometric ratio for angle A is the one that matches the side lengths as per the definitions above.