Question: Now use a calculator to find the inverse tangent of $\frac{73.7}{39.4}$, rounding to the nearest thousandth.
tan A = $\frac{73.7}{39.4}$
1. **State the problem:** Find the angle $A$ such that $\tan A = \frac{73.7}{39.4}$.
2. **Formula used:** To find the angle from a tangent value, use the inverse tangent function:
$$ A = \tan^{-1}\left(\frac{73.7}{39.4}\right) $$
3. **Calculate the ratio:**
$$ \frac{73.7}{39.4} \approx 1.87005 $$
4. **Apply the inverse tangent:**
$$ A = \tan^{-1}(1.87005) $$
Using a calculator,
$$ A \approx 61.012^\circ $$
5. **Round to the nearest thousandth:**
$$ A \approx 61.012^\circ $$
**Final answer:** The angle $A$ is approximately $61.012^\circ$.