An airpline flies 165 miles from point a in the direction 130degrees and then travels in the direction 245 degrees for 80 miles. approximately how far is the airplane from point a?

205.4 miles

Step-by-step explanation:

As per the question,

We have been provided that an airplane started flies 165 miles from point A  in the direction of 130 degrees and after that, it changes its direction to 245 degrees and travel to 80 miles again, which is drawn in the figure as below:

From the figure,

Let XY be the plane.

Now,

By using the cosine rule in triangle APR, we get

AP² = AR² + PR² - 2 × AR × PR × cos 115°

Now put the value from figure:

AP² = 165² + 80² - 2 × 165 × 80 × (-0.325)

AP² = 42205

AP = 205.4 miles.

Hence, the airplane is 205.4 miles far from point A.