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 17 degree. After flying for 91 miles, the helicopter flies due east for some time. The helicopter flies back to the airport with a bearing of 230 degree. How far did the helicopter fly on the final leg of its journey? The distance the helicopter flew was approximately miles. (Do not round until the final answer. Then round to the nearest tenth.)

Solution

It\'s a triangle problem
3 segments that form a triangle : segment1 of 91 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
17° is an angle calculated from Y for segment1
230° is the bearing on the compass to go back to airport and corresponds to 50° =(230° -180°) as angle calculated from Y in the first quadrant

so the first angle of the triangle is 50° - 17° = 33°
90° - 50° = 40° corresponds to another angle of the triangle
So we have the angles and a side
a=91 and opposite angle is 40°
b (segment to East) and opposite angle is 33°
c (segment back airport) and opposite angle is (180 -(50+33)) = 97°

law of the sinus in a triangle
c /sin97° = 91 /sin40° then c = 91(sin97°/ sin40°) = 140.5156miles