Question #85311

Jun 17, 2015

Resultant $= 5.7 \text{ m }$ 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:
${c}^{2} = {a}^{2} + {b}^{2} - 2 a b \cos C$

In our case, we can apply the rule thus:

Applying the rule:

${R}^{2} = {2}^{2} + {4}^{2} - 2 \left(2\right) \left(4\right) \cos \beta$

$\implies {R}^{2} = 20 - 16 \cos \left(143\right)$

$\implies R = \sqrt{20 - 16 \cos \left(143\right)}$

$R = 5.7 m$