Calculate LOG using the Sine Rule.

Step 1: Calculate $\angle LOG$ using the Sine Rule.
The Sine Rule states that for a triangle with sides $a, b, c$ and opposite angles $A, B, C$:

$$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$

In $\triangle OGL$, we have $LG = 10.1\,\text{m}$, $OG = 14.2\,\text{m}$, and $\angle OLG = 40^\circ$. We can find $\angle LOG$ (the angle at O) using the Sine Rule:

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