Q2 Exercise 4.2B: Trigonometry 1 David Rayner Complete Mathematics Extended Book Solution

🔺 Problem:

In a right-angled triangle:

• One angle is $61^\circ$
  

• The hypotenuse is $4$ units

• Find the length of side $b$, which is opposite the $61^\circ$ angle.

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✅ Step 1: Use the sine ratio

$$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ $$\sin(61^\circ) = \frac{b}{4}$$

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✅ Step 2: Solve for $b$

$$b = 4 \cdot \sin(61^\circ)$$
$$\sin(61^\circ) \approx 0.8746$$
$$b \approx 4 \cdot 0.8746 = 3.4984$$

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✨ Final Answer:

$$\boxed{b \approx 3.50 \text{ units}} \quad \text{(to 3 significant figures)}$$