To find the energy stored in the battery, follow these steps:

Convert mAh to Ah:

The battery capacity is given as 5800 mAh. Since

$$1\,\text{Ah} = 1000\,\text{mAh},$$

we have

$$5800\,\text{mAh} = 5.8\,\text{Ah}.$$

Calculate energy in watt-hours (Wh):

The energy in Wh is given by the product of the voltage and the capacity in Ah. Thus,

$$\text{Energy (Wh)} = 4.2\,\text{V} \times 5.8\,\text{Ah} = 24.36\,\text{Wh}.$$

Convert watt-hours to joules (J):

Since

$$1\,\text{Wh} = 3600\,\text{J},$$

the total energy in joules is:

$$24.36\,\text{Wh} \times 3600\,\text{J/Wh} = 87,696\,\text{J} \approx 87.7\,\text{kJ}.$$

Thus, the energy stored in the battery when fully charged is about 87.7 kJ.

The correct answer is Option A: 87.7 kJ.