A helicopter flies from the airport on a course with a beari

A helicopter flies from the airport on a course with a bearing of 15°. After flying for 104 miles, the helicopter flies due east for some time. The helicopter flies back to the airport with a bearing of 227°. How far did the helicopter fly on the final leg of its journey?

*(Do not round until the final answer. Then round to the nearest tenth.)

Solution

3 segments that form a triangle : segment1 of 104 miles, segment2 to east, segment3 (what you must calculate,back to airport)

You must understand that the angles are calculated from Y-axis for bearing in a plane
Y-up is North or 0°
Y-down is South or 180°
X-right is East or 90°
X-left is West or 270°
airport : center of axes

Ok
Let\'s find the angles of the triangle
15° is an angle calculated from Y for segment1
227° is the bearing on the compass to go back to airport and corresponds to 47° (227° -180°) as angle calculated from Y in the first quadrant

so the first angle of the triangle is 47° - 15° = 32°
90° - 47° = 43° corresponds to another angle of the triangle
So we have the angles and a side
a=104 and opposite angle is 43°
b (segment to East) and opposite angle is 32°
c (segment back airport) and opposite angle is 105°(180 -(43+32))

law of the sinus in a triangle
c /sin105° = 104 /sin43° then c = 104(sin105°/ sin43°) = 147.2969 miles = 147 miles