# Geometry

A ship sails 5 km from a port A on a bearing of 85 degrees and then 6 km on a bearing of 50 degrees. Calculate the distance and bearing from A.

1. 👍 0
2. 👎 0
3. 👁 656
1. calculate the horizontal and vertical replacements of each trip
first trip:
x/5 = cos85 , x = 5cos85
y/5 = sin85 , y = 5sin85

2nd trip:
x/6 = cos50 , x = 6cos50
y/6 = sin50 , y = 6sin50

total horizontal displacement
= 5cos85 + 6cos50 = appr 4.2925
total vertical displacement
= 5sin85 + 6sin50 = appr 9.5772

now use Pythagoras ... to get

√(4.2925^2 + 9.5772) = 40.4952

or

((5cos85,5sin50) + (6cos50,6sin50) and take their magnitude.

(the actual calculations are the same as above)

1. 👍 0
2. 👎 0
2. THANK YOU

1. 👍 0
2. 👎 0
3. Are we worried whether we use compass headings where North = 0 degrees, rather than East, and angles are measured clockwise?

1. 👍 0
2. 👎 0

## Similar Questions

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. ### math

A ship leaves port and travels 21km on a bearing of o32 degrees and then 45km on a bearing of 287 degrees. a. calculate its distance from the port. b. calculate the bearing of the port from the ship

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. ### Maths

A ship leaves a port and travels 21km on a bearing of 32 and then 45km on a bearing of 287 calculate its distance from the port and the bearing of the port from the ship

1. ### 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

2. ### 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.

3. ### Math

The bearing of ship A and B from a port P are 225 degree and 116 degree respectively.ship A is 3.9km from ship B on a bearing of 258 degree.calculate the distance of A from P.

4. ### 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

1. ### Trig

A ship leaves port with a bearing of S 40 W. After traveling 7 miles, the ship turns 90 degrees on a bearing of N 50 W for 11 miles. At that time, what is the bearing of the ship from port?

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. ### MATHS

A ship sails 95 km on a bearing of 140 degree,then a further 102 km on a bearing of 260 degree and then returns directly to its starting point.find the length and bearing of the return journey.

4. ### Triggggggg

A ship is 90 miles south and 20 miles east of port. The captain wants to travel directly to port. What bearing should be taken?