Trig

[dhthompson]

I understand how to work problems using law of cosines, but not sure about the wording. Two planes flying together in formation take off in different directions. One flies due east at 350 mph, and the other flies east north-east at 380 mph. How far apart are the two planes 2 hours after they separate (assuming that they fly at the same altitude).

Does that mean that the angle is 45 degrees?

 

[Deleted member 4993]

I understand how to work problems using law of cosines, but not sure about the wording. Two planes flying together in formation take off in different directions. One flies due east at 350 mph, and the other flies east north-east at 380 mph. How far apart are the two planes 2 hours after they separate (assuming that they fly at the same altitude).

Does that mean that the angle is 45 degrees?

The angle is 22.5°.

Try to use search engines - that's where I got the answer.

 

[soroban]

Hello, dhthompson!

Two planes flying together in formation take off in different directions.
One flies due east at 350 mph, and the other flies east north-east at 380 mph.
How far apart are the two planes 2 hours after they separate?

Does that mean that the angle is 45 degrees? . . . . no

The angle between E and NE is 45 degrees.

The angle between E and ENE is 22.5 degrees.

                      B
                      *
            760   *    \
              *         \
          * 22.5d        \
    O *   *   *   *   *   * A
               700

In two hours, the first plane flies 700 miles from point O to point A
. . . . .and the second plane flies 760 miles from point O to point B.

Use the Law of Cosines to find side AB.