Question: SINE AND COSINE RULES - PRACTICE QUIZ
1.
Use sine rule to find x to 1 decimal place.
x
13.9 cm
496
626
Graph shape: triangle in the center; left side is labeled x, right side is labeled 13.9 cm, with base angles 496 at bottom-left and 626 at bottom-right. position_hint=center
2.
Use sine rule to find y to 1 decimal place.User: answer
1. **Problem:** Use the sine rule to find $x$ in the triangle with sides and angles given: side opposite $49^\circ$ is $x$, side opposite $62^\circ$ is $13.9$ cm.
2. **Formula:** The sine rule states:
$$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$
where $a,b,c$ are sides opposite angles $A,B,C$ respectively.
3. **Identify known values:**
- Side $b = 13.9$ cm opposite angle $B = 62^\circ$
- Angle $A = 49^\circ$
- Side $a = x$ opposite angle $A$
4. **Apply sine rule:**
$$\frac{x}{\sin 49^\circ} = \frac{13.9}{\sin 62^\circ}$$
5. **Solve for $x$:**
$$x = \frac{13.9 \times \sin 49^\circ}{\sin 62^\circ}$$
6. **Calculate sines:**
$$\sin 49^\circ \approx 0.7547, \quad \sin 62^\circ \approx 0.8829$$
7. **Substitute values:**
$$x = \frac{13.9 \times 0.7547}{0.8829}$$
8. **Simplify fraction:**
$$x = 13.9 \times \frac{0.7547}{0.8829}$$
9. **Calculate fraction:**
$$\frac{0.7547}{0.8829} \approx 0.8549$$
10. **Final multiplication:**
$$x \approx 13.9 \times 0.8549 = 11.88$$
11. **Round to 1 decimal place:**
$$x \approx 11.9$$ cm
**Answer:** $x = 11.9$ cm