Bearings?!

[trigophobia]

Hi everyone!

So I kind of have a huge problem... We started with trigonometry two weeks ago and now reached bearings. I've done perfectly fine with it, as long as it only contained 1 bearing thingy. But in this exercise we had to use two of them.

Here's the task:

A yacht sails 15 km on a bearing of 053° and then 7 km on a bearing of 112°.
How far north is the yacht from its starting position.

See, I understood how I had to calculate the first part. But then after I got that (how far north it goes with a bearing of 053°), I couldn't seem to figure out how I had to construct a sketch and then calculate it to the correct result. Solution would be 6.40km

I would be so greatfull if any of you could help me get to that result!
Thanks in advance,
Joelle (

 

[HallsofIvy]

Hi everyone!

So I kind of have a huge problem... We started with trigonometry two weeks ago and now reached bearings. I've done perfectly fine with it, as long as it only contained 1 bearing thingy. But in this exercise we had to use two of them.

Here's the task:

A yacht sails 15 km on a bearing of 053° and then 7 km on a bearing of 112°.
How far north is the yacht from its starting position.

See, I understood how I had to calculate the first part. But then after I got that (how far north it goes with a bearing of 053°), I couldn't seem to figure out how I had to construct a sketch and then calculate it to the correct result. Solution would be 6.40km

I would be so greatfull if any of you could help me get to that result!
Thanks in advance,
Joelle (

You say you were able to find "how far north it goes with a bearing of 053°" so apparently you know how find "components". The first leg is 15 km at 53° so the north component is 15 cos(53) and the east component is 15 sin(53). Now do the same thing for the next leg, 7 km at 112° so the north component is 7 cos(112) and the east component is 7 sin(112).

Now something that has two (or more) "components" is a vector- and we add vectors by adding components- add the two north components and add the two east components to get the components of the whole voyage.