Question

A pilot flies in a straight path for 1 hour and 30 min. She then makes a course correction, heading 10 degrees to the right of her original course, and flies 2 hours in the new direction. If she maintains a constant speed of 655 miles per hour, how far is she from her starting position?

Answer 1

let she started from the point A and changed her direction from point B and finaly she is at point C

distance between A&B =1.5*655=982.5miles

dsitance between B&C=2*655=1310miles

as we can see point a,b&c forms a triangle

where AB=982.5

BC=1310

angle between AB&BC=180-angle correction made by pilot=180-10=170

so using cosine length of AC2 =AB2+BC2-2*AB*BC*cos(angle between AB&BC)

AC2=982.52+13102-2*982.5*1310*cos(170)

AC2=266867.058832

AC=516.59177 miles

so she is 517 miles away from starting point