# Precalculus

I did these problems by drawing a graph ... So it would be great if you do it that way too if you need to correct me.
I know this is overwhelming but please take your time... It is easier for me to post all of these at once,since I can find it easier rather than posting many posts...

1. 11 units at 0 degree followed by 5 units along a bearing of 70 degrees
My answer: 13.6 units at 20.1 degrees
2. 8 units at 90 degrees followed by 6 units along a bearing of 210 degrees
My answer: 7.21 units at 136 degrees
3. 6 units at 270 degrees followed by 14 units along a bearing of 110 degrees
My answer: 8.61 units I DO NOT UNDERSTAND HOW TO FIND THE ANGLE BECAUSE WHEN I USED THE LAW OF COSINES I GOT 146 DEGREES...SO AM I SUPPOSED TO DO THIS??: 180-146= acute angle....BUT THEN I DON'T GET WHICH DIRECTION SHOULD I ADD UP THE ANGLE THAT SMOOCHES AT THE RESULTANT VECTOR... IN OTHER WORDS, WHEN STARTING ON THE Y AXIS OR THE NORTH POSITION DO I GO RIGHT OR LEFT AND WHY??????????
4. 4 units at 180 degrees followed by 9 units along a bearing of 320 degrees
My answer: 6.47 units at 243 degrees
5. A ship sails 50 mi on a bearing of 20 degrees and then 30 mi further on a bearing of 80 degrees . Find the resultant displacement vector as a distance and bearing.
My answer : 70 miles at 41.8 degrees
6. A plane flies 200 mi/hr along a bearing if 320 degrees. The air is moving with a speed of 60 mi/hr along a bearing of 190 degrees.
My answer: 168 mi/hr at 304 degrees
7. A scuba diver swims 100 ft/min along a bearing of 170 degrees. The water is moving with a current of 30 ft/min along a bearing of 115 degrees.
My answer: 116 ft/min at 156.5 degrees
8. Given: 120 yards at 80 degrees and 22 yards at 10 degrees
My answer: 129 yards at 70.8 degrees

1. first off, you move along a heading.
If you see something and determine its position, then the bearing is the direction from where you are.
Now on to the calculations.

#1. ok
#2. ok
#3. I do mine by converting each position to rectangular coordinates, then adding the vectors, then converting back to polar coordinates. Keeping in mind that a compass heading of x° is a polar angle of (90-x)°
So, for this one, I do
6@270° = -6,0
14 @ 110° = 13.16,-4.79
add them up to get 7.16,-4.79
d = 8.61
θ = -33.8
Using the law of cosines does get tricky.
#4. I get 6.47 at 296.6°
#5. I get 32.8 at 72.4°
#6. ok
#7. ok
#8. ok

posted by Steve

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