Two ships leave a port at the same time

Question

Two ships leave a port at the same time, the first on a bearing of 65^o, the second on a bearing of 155^o. After one hour, the first boat traveled 20 nautical miles while the second boat traveled 25 nautical miles. how far apart are the two ships? round your answer to the nearest tenth.

Answer 1

P- port (Origin of x-y plan)

PA - distance from point P (port) and 1-st ship after 1-st hour (straight line)

PB - distance from point P (port) and 2-nd ship after 1-st hour (straight line)

Find BA, distance between ships after 1-st hour.

Note that the angle between PA and axis "y" (positive portion) is 25º (90º - 65º).

The angle for 2-nd ship was 155º, i.e. 90º + 65º, and it means the angle BPA is 65º + 25º = 90º

Then BPA is the right triangle with two sides 20 and 25.

20/25 = 4/5

Therefore, 2-nd leg of triangle should have this relationship with other sides:

3:4:5

Scale factor is "5"

3 • 5 = 15

BA = 15

(note that 15, 20, 25 are Pythagorean triples).

Answer 2

Draw and label a diagram!

The angel between the bearings of the two ships is 90°.

Use Pythagoras to determine the distance.