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An airplane leaves airport \(A\) and travels 520 miles to airport \(B\) at a bearing of \(N 35^{\circ} W\). The plane leaves airport \(B\) and travels to airport \(C 310\) miles away at a bearing of \(S 65^{\circ} W\) from airport \(B\). Find the distance from airport \(A\) to airport \(C\).

Two planes take off at the same time from an airport. The first plane flies at \(300 \mathrm{mph}\) at a bearing of \(S 45^{\circ} E .\) The second plane is flying at a bearing of \(S 5^{\circ} \mathrm{W}\) with a speed of \(330 \mathrm{mph}\). How far apart are they after 3 hours?

A ship leaves the entrance to a harbor and travels 15 miles with a bearing \(S 10^{\circ} W\), then turns and travels 45 miles with a bearing of \(N 43^{\circ} W\). How far from the harbor entrance is the ship and what is the bearing of the ship from the harbor?

A tree on a hillside casts a shadow \(208 \mathrm{ft}\) down the hill. If the angle of inclination of the hillside is \(25^{\circ}\) to the horizontal and the angle of elevation of the sun is \(51^{\circ}\), find the height of the tree.