# Math

Two ships leave port at 4 p.m. One
is headed N38°E and is travelling at
11.5 km/h. The other is travelling at
13 km/h, with heading S47°E. How far
apart are the two ships at 6 p.m.?

i am in grade 11 :), studying ahead of the class :) its 8 pm here, this question is hard for me, i spent 10 minutes on it.

1. 👍
2. 👎
3. 👁
1. draw the diagram, figure each distance (velocity*time). time is 2 hours for each ship

Now you have a triangle, 2 known legs, and the included angle.

Find the opposite side: I recommend use the law of cosines.

1. 👍
2. 👎
👤
bobpursley
2. The standard graph in polar coordinates has E at 0' ( o degree ) .
The makes N 38 E would be 90'- 38' = 52' and S 47 E at 2700'+ 47'= 314' , or -46 .
The difference in angle between the two is 53+46= 99'
At 6 PM , two hours have passed . This means the 1st ship went 2(11.5)=23 miles and the 2nd ship went 2(13)= 26 miles . Here , a= 23 , B=26 and A= 99'

This is the only way I can help , I am in 11th grade but I already did some excercise like this , not this one but some like it . I am a Haitian student , ( Haiti) so please maybe my English don't realy make you understand it because I do it in French at school but I translate it in English for you . This is the way they learn me to do it !!! Good luck Karen , be smart !!! Study hard !

1. 👍
2. 👎
3. Unless otherwise indicated, all angles
are measured CCW from +x-axis.

Ship #1:
d1 = 11.5km/h[52o] * 2h = 22km[52o].

Ship #2:
d2 = 13km/h[ 317o] * 2h = 26km[317o].

d2-d1 = 26[317o] - 22[52o].

X = 26*Cos317 - 22*Cos52) = 5.47 km.
Y = 26*sin317 - 22*sin52 = -35.1 km.

d2-d1 = Sqrt(X^2 + Y^2) = Distance apart.

1. 👍
2. 👎

## Similar Questions

1. ### trig

Help! Ships A and B leave port at the same time and sail on straight paths making an angle of 60 degrees with each other. HOw far apart are the ships at the end of 1 hour if the speed of ship A is 25 km/h and that of ship B is 15

2. ### Math

Two ships leave the same port at the same time. One ship sails on a course of 110 degree at 32 mi/h. The other sails on a course of 230 degree at 40 mi/h. Find the distance between them after 2 hours. Express your answer to the

3. ### trig

It is 4.7km from Lighthouse A to Port B. The bearing of the port from the lighthouse is N73E. A ship has sailed due west from the port and its bearing from the lighthouse is N31E. How far has the ship sailed from the port?

4. ### Trigonometry

An observer on a cliff 1000 dm above sea level sights two ships due east. the angles of depression of the ships are 44o and 32o. Find the distance between the ships.

1. ### Calculus

Two ships leave the same port at noon. Ship A sails north at 22 mph, and ship B sails east at 12 mph. How fast is the distance between them changing at 1 p.m.? (Round your answer to one decimal place.)

2. ### Trig

Two ships leave the same port at 7.am. The first ship sails towards europe on a 54 degree course at a constant rate of 36 mi/h. The second ship,neither a tropical destination, sails on a 144 degree course at a constant speed of 42

3. ### trig

Two ships, one sailing at 30 km/hr and the other at 45 km/hr, left port at the same time. Three hours later they were 120 km apart. If you had to find the angle between their courses an equation that could be used to solve this

4. ### Trig

Two ships leave a harbor at the same time. One ship travels on a bearing S11 degrees W at 12 mph. The second ship travels on a bearing N75 degrees E at 9 mph. How far apart will the ships be after 3 hours?

1. ### math

Two ships leave a port at 9 a.m. One travels at a bearing of N 53° W at 12 miles per hour, and the other travels at a bearing of S 67° W at 19 miles per hour. Approximate how far apart they are at noon that day. (Round your

2. ### math

A boat travels from one port A to port B, travelling 126 km, upstream (against the current) at a uniform speed, and the trip takes 6 hours. On the way back (downstream), the trip only takes 4.5 hours. Set up and solve a system of

3. ### I NEED URGENT HELP!!!

A ship leaves port at 1:00 P.M. and sails in the direction N36°W at a rate of 25 mi/hr. Another ship leaves port at 1:30 P.M. and sails in the direction N54°E at a rate of 16 mi/hr. (a) Approximately how far apart are the ships

4. ### math

Two ships leave a port at 9 a.m. One travels at a bearing of N 53° W at 12 miles per hour, and the other travels at a bearing of S 67° W at 19 miles per hour. Approximate how far apart they are at noon that day. (Round your