Q1 Exercise 4.2B: Trigonometry 1 David Rayner Complete Mathematics Extended Book Solution

🔍 Given:

• Angle = 27°

• Hypotenuse = 10 cm

• Right angle at the corner

• Need to find side a, which is opposite the 27° angle

---

📐 Using the sine function:

$$\sin (\theta )=\frac{\text{opposite}}{\text{hypotenuse}}$$$$\mathrm{<br>}\sin ({27}^{\circ })=\frac{a}{10}$$$$\mathrm{<br>}a=10\times \sin ({27}^{\circ })$$$$\mathrm{<br>}a\approx 10\times 0.4540=4.540$$

---

✅ Answer (to 3 significant figures):

$$\boxed{{\displaystyle a\approx 4.54\text{ cm}}}$$