What american strength did yamamoto hope to weaken in attacking midway?

Due to their advanced code-breaking abilities, the United States was able to predict what the Japanese's attack strategy on Pearl Harbor. The U.S. strategically moved their aircraft carriers to avoid the attack and were able to advance on the Japanese Navy. 

The aircraft carriers then became the focus of Japan's military strategy. They were upset that their plans were interrupted and didn't work the first time, so they gave it another try. The Japanese fleet commander, Admiral Yamamoto, chose Midway since it was close to Pearl Harbor. His goal was to destroy the American aircraft carriers. He hoped that this tactic would move them away from the rest of the U.S. forces and be the best place to eliminate the carriers. 

Remember soh-cah-toasoh: cah: toa: now, looking at the picture we can see that we have an angle, the hypotenuse and want to find the value of the adjacent side to the angle. so we use cah to find the adjacent angle. plug in what we have: we need to solve for x now so we get it by itself on one side: plug this into your calculator and you'll find that: