Thread: Find the distance

A ship travels 55 km on a bearing of 27 degree, then travels on a bearing of 117 degree for 140 km. Find the distance traveled from the starting point to the ending point.
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What I did is following:
sin27=55/hypotenuse
cos63=55/hypoenuse
*****>>>>these two give me 121 km
cos27=140/hypotenuse
Sin63=140/hypotenuse
*****>>>>>these two give me 157 km
But if I used the pythagorean thm, it gives me 150 km

I have seen similar problems they used sometimes, cos or sin or solve by pythagoran thm........It's confusing when to use what?

from your explanation I found you could just use the pythagoras theorem with 55 and 140 as the shorter sides as the turn of the ship was exactly 90 degrees, therefore

distance travelled

The 157 could've resulted in rounding error introduced from using the trig functions.

Originally Posted by Judi

A ship travels 55 km on a bearing of 27 degree, then travels on a bearing of 117 degree for 140 km. Find the distance traveled from the starting point to the ending point.
******************************************
What I did is following:
sin27=55/hypotenuse
cos63=55/hypoenuse
*****>>>>these two give me 121 km
cos27=140/hypotenuse
Sin63=140/hypotenuse
*****>>>>>these two give me 157 km
...

Have you made a sketch?

The bearings are outside of the triangle in question. Therefore your method will not provide you with a valid result.