The captain of a ship sights a lighthouse on a bearing 060° (N 60°E) and at the same time sights a buoy on a bearing
051° (N 51°E). He knows the buoy is 1.3 miles from the
lighthouse on a bearing of 340° (N 20°W) from the
lighthouse to the buoy. Find to the nearest tenth of a mile
the distance from the ship to the buoy.

Aspacecraft can attain a stable orbit 300 kilometers above earth if it reaches a velocity of 7.7 kilometers per second. the formula for a rocket's maximum velocity v in kilometers per second is vequalsminus0.0098tplusc ln upper r, where t is the firing time in seconds, c is the velocity of the exhaust in kilometers per second, and r is the ratio of the mass of the rocket filled with fuel to the mass of the rocket without fuel. find the velocity of a spacecraft whose booster rocket has a mass ratio of 20, an exhaust velocity of 2.1 km/s, and a firing time of 15 s. can the spacecraft achieve a stable orbit 300 km above earth?