Question

Trying to learn how to apply the Laws os Sines and Cosines in a problem

Answer 1

Recall

Solution

Using cosine rule

$a^2=b^2+c^2-2bc\text{ cosA}$$\begin{gathered} x^2=180^2+200^2-2\times180\times200\times cos75 \\ x^2=32400+40000-18634.9712 \\ x^2=53765.02876 \\ x=\sqrt{53765.02876} \\ x=231.87287 \\ \end{gathered}$

The final answer

$232m\text{ \lparen nearest integer\rparen}$