Question

An aircraft on a reconnaissance mission takes off from its home base and flies 550 miles at a bearing of S 46° E to a location in the sea. It then flies 483 miles from the sea at a bearing of S 55° W to another location. Finally, the aircraft flies straight back from the second location to its base. What is the total distance it flies, rounded to the nearest mile?

Answer 1

Answer:

1692 is the answer

Step-by-step explanation:

Answer 2

Check the picture representing the movement of the aircraft.

Let B be the base, A is the first location and C is the second location.

The angles of the directions S 46° E and S 55° W are as shown in the figure.



The measure of angle BAC is (90°-46°)+(90°-55°)=44°+35°=79°.

According to the cosine law, we have:

$|BC|^2=|BA|^2+|AC|^2-2 \cdot|BA| \cdot |AC| \cdot cos 79^o\\\\|BC|^2=550^2+483^2-2 \cdot 550 \cdot 483 \cdot 0.19\\\\|BC|^2=302,500+233,289-100,947\\\\|BC|^2=434,842\\\\|BC|= \sqrt{434,842}\approx 659 (miles)$

Answer: 659 miles