Two cities, A and B are 300 miles apart. In flying fromcity A to city B, a pilot

Question

Two cities, A and B are 300 miles apart. In flying fromcity A to city B, a pilot inadvertently took a course that was 5degrees in error.

(a) If the error was discovered after flying 10 minutes at aconstant spped of 420 miles per hour, through what angle should thepilot turn to correct the course?

(b) What new constantspeed should be maintained so that no time is lost due tothe error? Assume that the speed would have been a constant420 miles per hour if no error had occurred.

See picture below.

Let E = location where error was discovered

Explanation / Answer

AE = 420 * (10/6) = 70 miles

tan (theta) = AB sin (5) / (AB cos(5) - AE)

= 300 sin(5 deg) / (300 cos (5 deg) - 70)

= 0.1142

Theta = atan(0.1142) = 6.514 degrees

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