1. The problem asks to approximate $\cot 50^\circ$ using technology and round the answer to the nearest hundredth. 2. Recall that $\cot \theta = \frac{1}{\tan \theta}$. 3. First, calculate $\tan 50^\circ$ using a calculator or technology. 4. Using a calculator, $\tan 50^\circ \approx 1.19175359$. 5. Then, $\cot 50^\circ = \frac{1}{\tan 50^\circ} \approx \frac{1}{1.19175359}$. 6. Simplify the fraction: $$\cot 50^\circ \approx \frac{1}{1.19175359} \approx 0.8391$$ 7. Round to the nearest hundredth: $$\cot 50^\circ \approx 0.84$$ Therefore, the approximate value of $\cot 50^\circ$ rounded to the nearest hundredth is $0.84$.