In the diagram below triangle EFG has a right angle at f.

In the right-angled triangle EFG:

• Angle F is $90^\circ$.
• Side EF is opposite to angle G, so $\text{opposite} = a$.
• Side FG is adjacent to angle G, so $\text{adjacent} = FG$.
• Side EG is the hypotenuse, so $\text{hypotenuse} = EG$.
• Angle G is $\phi$.

The tangent of an angle in a right-angled triangle is the ratio of the length of the opposite side to the length of the adjacent side.

$$\tan(\phi) = \frac{\text{opposite}}{\text{adjacent}}$$

Substitute the known values:

$$\tan(\phi) = \frac{EF}{FG} = \frac{a}{FG}$$

Rearrange the equation to solve for FG:

$$FG = \frac{a}{\tan(\phi)}$$

The length of side FG is $\boxed{\mathbf{\frac{a}{\tan(\phi)}}}$

The sine of an angle in a right-angled triangle is the ratio of the length of the opposite side to the length of the hypotenuse.

$$\sin(\phi) = \frac{\text{opposite}}{\text{hypotenuse}}$$

Substitute the known values:

$$\sin(\phi) = \frac{EF}{EG} = \frac{a}{EG}$$

Rearrange the equation to solve for EG:

$$EG = \frac{a}{\sin(\phi)}$$

The length of side EG is $\boxed{\mathbf{\frac{a}{\sin(\phi)}}}$