Hello protractor

Welcome to Math Help Forum! Originally Posted by

**protractor** hello,

I haven't found out how to complete my profile yet, so- I am a 54 year old woman, with 2 grown up children, I study Maths at home, mainly from 2nd hand Maths books I've bought in charity shops, although sometimes I have to buy a new one. I was average at Maths at school, just about got an O level, but have become much much better as an adult, and I'm absolutely sure that by dint of persistent studying my brain has actually physically changed, I'm so much better now!

But now I'm stuck again . It's a question from an AS Maths text book. I've tried to draw a diagram of it, but I keep getting confused and going round in circles and I'm not sure what to put where, it's worse than being stuck out in the Pacific for days without food or water, not knowing which way to turn, and I'm becoming hysterical over it

Here it is:

Find the magnitude and direction of the resultant of the two given vectors: A displacement of magnitude 3.5 km on a bearing 50 degrees, and a displacement of magnitude 5.4 km on a bearing of 128 degrees.
In the text book, the ANSWER is given as: 7.02 km and 98.9 degrees.

Take a look at the diagram I've attached. You'll see that each angle is measured clockwise from the North. Can you see that this will give:$\displaystyle \angle ABC = 360 - (130 + 128) = 102^o$

So now you use the Cosine Rule on the triangle to get:$\displaystyle AC^2 = 3.5^2 + 5.4^2 - 2\times3.5\times5.4\cos102^o$

This will give the answer

$\displaystyle AC = 7.02$ km (Can you work that out?)

Then use the Sine Rule to work out $\displaystyle \angle BAC$, and add $\displaystyle 50^o$ to get the bearing of $\displaystyle AC=098.8^o$.

Can you complete it now?

Grandad