# Trigonometry

posted by .

If a ship leaves port at 9:00 a.m. and sails due south for 3 hours at 14 knots, then turns N 60° E for another 2 hours, how far from port is the ship?
A. 14 nm
B. 17.75 nm
C. 21.5 nm
D. 22.6 nm

• Trigonometry -

looks like a rather straight-forward case of the cosine law.
distance^2 = 42^2 + 28^2 - 2(42)(28)cos60
= 1372
distance = 37.04 nm

or

vector of first leg = (42cos270, 42sin270)=(0, -42)
vector for 2nd leg = (28cos30,28sin30) = (24.249, 14)
adding them to get (24.249 , -28)
magnitude = √(24.249^2 + (-28)^2) = √1372 = 37.04 nm

My answer was obtained in 2 totally different methods

• Trigonometry -

Wel, I'm not sure, I have two other questions with practically the same things, please take a look!
If a ship leaves port at 9:00 a.m. and sails due east for 3 hours at 10 knots, then turns N 60° E for another hour, how far from port is the ship?
A. 35 nm
B. 39 nm
C. 43 nm
D. 47 nm
__________________________________
If a ship leaves port at 9:00 a.m. and sails due south for 3 hours at 14 knots, then turns N 60° E for another 2 hours, how far from port is the ship?
A. 14 nm
B. 17.75 nm
C. 21.5 nm
D. 22.6 nm
_____________________________
Thank you; you'tr a life saver!

• Trigonometry -

If a ship leaves port at 9:00 a.m. and sails due north for 3 hours at 12 knots, then turns N 30° E for another hour, how far from port is the ship?
A. 45 nm
B. 47 nm
C. 51 nm
D. 53 nm

• Trigonometry -

This time I get a triangle with sides 30 and 10 and the contained angle between them is 150° , (90+60)

again by the cosine law,
dist^2 = 30^2 + 10^2 - 2(30)(10)cos150
= 1519.62
distance = √1519.62 = appr 38.98 nm
which is choice B

The next question you posted is a repeat of your first

The third:
same setup;
dist^2 = 36^2+ 12^2 - 2(36)(12)cos150
= 2188.25
dist = 46.78 which looks like it is B.

Something fishy about your first one, since I followed exactly the same steps

• Trigonometry -

Thank you very much; but these are the only answers! I don't know why, but I'll try to check with my teacher. Again, thanks for the help and showing your work, you're awesome!

• Trigonometry -

Just tried you first question again, using cos30° in my cosine law
and got 22.6 which is D

BUT, according to your wording of N 60° E, the angle between the two paths would be 60, and not 30

So to get your answer it should have been N 30° E

## Similar Questions

1. ### math- precalculus

I've attempted this problem a few times but I can't get the right answer. Can someone show me how I can do it?
2. ### geometry

A ship leaves port and heads due east at a rate of 32 miles per hour. Ever since the ship left port, it has been pushed south by a strong constant wind. Five hours after leaving port, the ship is 200 miles away. What is the effective …
3. ### Math

"A ship leaves port on a bearing of 34.0 degrees and travels 10.4 mi. The ship then turns due east and travels 4.6 mi. How far is the ship from port, and what is its bearing from port?
4. ### Trigonometry

Navigation A ship leaves port at noon and has a bearing of S 29° W. If the ship sails at 20 knots, how many nautical miles south and how many nautical miles west will the ship have traveled by 6:00 P.M.?
5. ### Trigonometry

A ship leaves port at 2:00 pm and sails in the direction S34 degrees W at a rate of 15mph. Another ship leaves port at 3:00 pm and sails in the direction S56 degrees E at a rate of 12mph. Find how far apart the ships are at 4:00 pm.
6. ### Math

A ship leaves port and sails northwest for 2 hours, and then sails N35degreesE for three hours. If it does not change speed, what direction must the ship sail to return directly to port?
7. ### trigonometry

A ship leaves its home port and sails on a bearing N38°15'E at 24 mph.At the same instant,another ship leaves the same port on a bearing S51°45'E at 28 mph.Find the distance between the two ships after 8 hours.
8. ### trig

If a ship leaves port at 9:00 a.m. and sails due north for 3 hours at 12 knots, then turns N 30° E for another hour, how far from port is the ship?
9. ### trig

If a ship leaves port at 9:00 a.m. and sails due south for 3 hours at 14 knots, then turns N 60° E for another 2 hours, how far from port is the ship?
10. ### Math Trigonometry

A ship leaves port and sails at a bearing of 124degrees. Another ship leaves the same port at the same time sailing at a bearing of 74degrees. When both ships are 80 miles from the port, how far are they from each other?

More Similar Questions