Mathematics — AI-generated practice question

Given: $\tan A = \dfrac{4}{3}$, so the side opposite to A = 4, side adjacent to A = 3.

Finding the hypotenuse using Pythagoras theorem:

$$\text{Hypotenuse}^2 = 4^2 + 3^2 = 16 + 9 = 25$$

$$\text{Hypotenuse} = 5$$

Finding sin A and cos A:

$$\sin A = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{4}{5}$$

$$\cos A = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{3}{5}$$

Source: Chapter 8, Section 8.1 (Trigonometric Ratios)

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• Examiners expect you to explicitly state the sides from tan A before applying Pythagoras — don't skip this step.
• The key identity used: $\text{Hypotenuse}^2 = \text{opposite}^2 + \text{adjacent}^2$ (Pythagoras theorem). Mentioning this by name earns the method mark.
• Final answers must use the standard ratio definitions from the summary: opposite/hypotenuse and adjacent/hypotenuse. All three steps (sides, hypotenuse, ratios) carry 1 mark each in a 3-mark question.