SHOW ALL WORK A pilot takes off from an airport and flies due east at a speed of $150k\frac{m}{h}$ for one hour. Then,

to avoid bad weather, they turn towards the north, and notify air traffic control that they have

turned $45$ to the north and are continuing at a speed of $150k\frac{m}{h}.$ Unfortunately, after one hour

they run into bad weather anyway and are forced to make an emergency landing. The landing site

is $75km$ north and $225\sqrt[\phantom{2}]{3}km$ east of the airport. Investigators determine that one of the plane's

navigational instruments gave an incorrect reading. Was the faulty instrument the compass or the

speedometer? How far off from the correct reading was it$?$ You may ignore altitude and assume

all speeds are relative to the ground.