Question: User: $(100 \tan 24^\circ) / (\tan 45^\circ 50' - \tan 24^\circ) + \tan 45^\circ 50'$
1. **State the problem:**
Calculate the value of the expression $$\frac{100 \tan 24^\circ}{\tan 45^\circ 50' - \tan 24^\circ} + \tan 45^\circ 50'$$.
2. **Convert angles to decimal degrees:**
$$45^\circ 50' = 45 + \frac{50}{60} = 45.8333^\circ$$
3. **Calculate the tangent values:**
$$\tan 24^\circ \approx 0.4452$$
$$\tan 45.8333^\circ \approx 1.0211$$
4. **Calculate the denominator:**
$$\tan 45.8333^\circ - \tan 24^\circ = 1.0211 - 0.4452 = 0.5759$$
5. **Calculate the fraction:**
$$\frac{100 \times 0.4452}{0.5759} = \frac{44.52}{0.5759}$$
6. **Simplify the fraction showing cancellation:**
$$\frac{\cancel{44.52}}{\cancel{0.5759}} = 77.29 \text{ (approx)}$$
7. **Add the last term:**
$$77.29 + 1.0211 = 78.31 \text{ (approx)}$$
**Final answer:** $$78.31$$