A boat sailing from A to B travels in a straight line until the captain realises he is off course. The boat is turned through an angle of 60 degrees, then travels another 10 km to b. the trip would have been 4 km shorter if the boat had gone straight from a to b. how far did the boat travel?

Question

mathmale · Answer

I found it essential to sketch this situation and to assign literals (letters) to represent the unknown lengths.

anonymous · Answer

im trying to draw the diagram out on here, but whenever i click the draw sign, nothing pops out D: i have a triangle ABC with CB=10km and angle ZCB as 120 degrees. I set my AB as x+4, and AC as x

mathmale · Answer

Same problem here.  Can't get the Draw utility to function! Darn!
I was going to establish x- and y-axes and let the origin be the starting point.  The pilot supposedly sails x units east (that is, along the x-axis in the positive direction) before realizing that he's off course.  He then turns 60 degrees to the north and sails for 10 km on that new course.  I think you accidentally typed ZCB when you meant angle ACB.  Yes, ACB is of 120 degrees, and CB is 10 km.
If you drop a line straight down (south) from point B, you will have formed a 30-60-90 triangle with hypotenuse 10 km.  The shorter leg will be 5 km and the longer (vertical) leg will be 5Sqrt(3) km, right?

Let the hypotenuse (AB) be y km in length.  Then side AC PLUS side BC add up to 4 more than y, or, in other words, AC plus 10 km sums up to y+4.

Hope this helps.  Suggest you draw all of this on paper.

I obtained AC=37 km, AB=38 km.

anonymous · Answer

@mathmale ughhh i just cant visualize what you said about drawing a line down south from point B. perhaps our points are not in the same places??? thanks for the detailed help though!