Question: Find the value of $m$. (1 d.p.)
17
50^\circ
m
Right triangle in the center-left: the left vertical side is $17$, the bottom side is horizontal, the slanted hypotenuse is labeled $m$, and the angle at the top-left between the vertical side and hypotenuse is $50^\circ$.
1. **Problem statement:** We need to find the length of the hypotenuse $m$ in a right triangle where the vertical side adjacent to the $50^\circ$ angle is $17$ units.
2. **Formula used:** In a right triangle, the adjacent side to an angle $\theta$ and the hypotenuse $m$ are related by the cosine function:
$$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{17}{m}$$
3. **Rearranging the formula to solve for $m$:**
$$m = \frac{17}{\cos(50^\circ)}$$
4. **Calculate $\cos(50^\circ)$:**
Using a calculator, $\cos(50^\circ) \approx 0.6428$
5. **Substitute and calculate $m$:**
$$m = \frac{17}{0.6428}$$
6. **Simplify the fraction:**
$$m \approx 26.45$$
7. **Round to 1 decimal place:**
$$m \approx 26.5$$
**Final answer:** The length of the hypotenuse $m$ is approximately $26.5$ units.