Given triangle OGL with LG = 10.1 m, OG = 14.2 m, and OLG = 40^.

Here are the solutions to your questions:

a)
Given triangle OGL with $LG = 10.1 \text{ m}$, $OG = 14.2 \text{ m}$, and $\angle OLG = 40^\circ$.

a)(i) Calculate angle OGL.

Step 1: Use the Sine Rule to find $\angle LOG$.
The Sine Rule states $\frac{a}{\sin A} = \frac{b}{\sin B}$. For $\triangle OGL$, we have:

$$\frac{LG}{\sin(\angle LOG)} = \frac{OG}{\sin(\angle OLG)}$$

Substitute the given values:

$$$$