please please please help

[yasmine03]

In attempting to fly from Chicago to Louisville, a distance of
80 miles, a pilot inadvertently took a course that was 9 degress in
error. If the aircraft maintains a speed of 120 miles per hour and
if the error in direction is discovered after 15 minutes through
what angle should the pilot turn to head towards Louisville?

 

[galactus]

There are various ways to tackle this. Let's try the law of cosines:

\(\displaystyle \sqrt{(80^{2})+(30^{2})-2(80)(30)cos(9)}=50.5875\)=side a.

Now, since we know that, we could just as well use the law of sines, but I am going to use the law of cosines again. What the heck.

\(\displaystyle 80^{2}=50.5875^{2}+30^{2}-2(50.5875)(30)cos(B)\)

\(\displaystyle =\frac{80^{2}-50.5875^{2}-30^{2}}{-2(50.5875)(30)}\)

\(\displaystyle =-.968916841693\)

I accidentally mislabelled my triangle. That second b up by the 50.59 should be side a.

\(\displaystyle cos^{-1}(-.986816841693)=165.677\) degrees.

Subtract from 180 to get 14.323 degrees toward Louisville.

 

[Denis]

In attempting to fly from Chicago to Louisville, a distance of
80 miles, a pilot inadvertently took a course that was 9 degress in
error. If the aircraft maintains a speed of 120 miles per hour and
if the error in direction is discovered after 15 minutes through
what angle should the pilot turn to head towards Louisville?

After 15 minutes plane travelled 30 miles (15/60 * 120, ok?)
30 becomes the hypotenuse of a right triangle with angles 90, 9 an 81 degrees.
30sin(9) = shorter leg. Use Pythagorean to get other leg. Can you carry on ?