Help please,

1) Two points A and B are on opposite sides of a building. A surveyor chooses a third point C 80 yd from B and 99 yd from A, with angle ACB measuring 59.1°. How far apart are A and B (to the nearest yard)?

2) Two airplanes leave an airport at the same time, one going northwest(bearing 135 degrees) at 418 mph and the other going east at 330 mph. How far apart are the planes after three hours(to the nearest miles)?

( or this I got 1782mi and then 692 mi but I feel neither of these are correct.)

Question

Help please,

1) Two points A and B are on opposite sides of a building. A surveyor chooses a third point C 80 yd from B and 99 yd from A, with angle ACB measuring 59.1°. How far apart are A and B (to the nearest yard)?

2) Two airplanes leave an airport at the same time, one going northwest(bearing 135 degrees) at 418 mph and the other going east at 330 mph. How far apart are the planes after three hours(to the nearest miles)?

( or this I got 1782mi and then 692 mi but I feel neither of these are correct.)

mathstudent55 · Answer

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anonymous · Answer

would it be 2076 mi?

mathstudent55 · Answer

One method is to use the law of cosines.
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mathstudent55 · Answer

Correct.
I did it two ways and got that answer.

anonymous · Answer

Thank you It turns out I multiplied them wrong on the first step.

mathstudent55 · Answer

Second method is to use the Pythagorean theorem after doing what I did in figure below.
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mathstudent55 · Answer

You're welcome.

mathstudent55 · Answer

Do you still need help with the first problem?

anonymous · Answer

No I Just figured it out thanks!

mathstudent55 · Answer

Great.
you're welcome.