The problem asks to convert the angle $115^\circ 120''$ to decimal degrees.

1. Problem Description

The problem asks to convert the angle $115^\circ 120''$ to decimal degrees.

2. Solution Steps

First, we need to convert the seconds to degrees.

We know that 1 degree is equal to 60 minutes and 1 minute is equal to 60 seconds. Therefore, 1 degree is equal to $60 \times 60 = 3600$ seconds.

To convert 120 seconds to degrees, we divide by 3600:

$120'' = \frac{120}{3600}^\circ = \frac{1}{30}^\circ$

Now, we convert the fraction to a decimal:

$\frac{1}{30} = 0.03333...$

Rounding to five decimal places, we have $0.03333^\circ$.

Next, we add this value to the degrees:

$115^\circ + 0.03333^\circ = 115.03333^\circ$.

3. Final Answer

$115.03333^\circ$