Math Question

Archimedes went to sleep beside a big rock. He wanted to get up at \( 7 \mathrm{AM} \), but the alarm clock was yet to be invented! He decided to sleep at the spot where the rock's shadow should end when it's 7 AM so as to be awakened by the direct sunlight.
Archimedes knew that at 7 AM, the sunlight reaches the ground at an angle of \( 31 \% \) The rock beside which he slept was 5 meters tall.
How far from the rock did Archimedes go to sleep?
Round your final answer to the nearest hundredth.



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