Question #85311

1 Answer
Jun 17, 2015

Answer:

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:

enter image source here

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#