A Diving Dilemma!

Geometry Level pending

I was at sea with my crew when we detected a treasure chest! The radar precisely detected the angle between our ship and the treasure was precisely \(53.13010235°\). Since I was the fastest swimmer (swimming at a rate of \(30 km/h\)), I volunteered to go get it. After getting my gear on, I descended to the angle which the computer told me. After 10 minutes, I reached the treasure. Hurrah! Facing the horizontal direction from which I came, and starting with my stomach against the ocean floor, I turned \(65°\) upwards, and ascended to the ship. However, it was not my ship! It was that of pirates, and I needed to contact the captain and alert him of the pirates!

The question is, how far away is the pirates' ship from mine (in km.)? Round to the nearest tenth.

Details & Assumptions

  • The sea floor is completely flat.

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