Question: Find the value of $m$. (1 d.p.)
$m$
26
43°
top-left: right triangle with a right angle at the bottom-left; the slanted side is labeled 26 and the bottom-right angle is 43°; the left vertical side is labeled $m$. solve this using SOH CAH TOA
1. **State the problem:** We need to find the length $m$ of the vertical side in a right triangle where the hypotenuse is $26$ and the angle opposite to $m$ is $43^\circ$.
2. **Recall the trigonometric ratio:** Using SOH CAH TOA, since $m$ is opposite the angle $43^\circ$ and the hypotenuse is $26$, we use sine:
$$\sin(43^\circ) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{m}{26}$$
3. **Set up the equation:**
$$\sin(43^\circ) = \frac{m}{26}$$
4. **Solve for $m$:**
$$m = 26 \times \sin(43^\circ)$$
5. **Calculate $\sin(43^\circ)$:**
$$\sin(43^\circ) \approx 0.6820$$
6. **Multiply:**
$$m = 26 \times 0.6820 = 17.732$$
7. **Round to 1 decimal place:**
$$m \approx 17.7$$
**Final answer:**
$$\boxed{17.7}$$