Question

Question #85311

Answer 1

Resultant `=5.7" m "` rounded to 2 significant figures

Explanation:

We use the technique called the cosine rule(or the rule of cosines)

Imagine, that the parrallelogram on the far right of the picture were divided into 2 equal triangles.
Now say, the sides were labelled `a,b,c` and the corresponding angles were `A,B,C` respectively.

Then the cosine rule could be stated as:
`c^2=a^2+b^2-2abcosC`

In our case, we can apply the rule thus:

Applying the rule:

`R^2=2^2+4^2-2(2)(4)cosbeta`

`=>R^2=20-16cos(143)`

`=>R=sqrt(20-16cos(143))`

`R=5.7m`