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

    just add the vectors
    ((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

Respond to this Question

First Name

Your Response

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?

You can view more similar questions or ask a new question.