With the help of tables, find the values, correct to places of decimals, of each of the following :
`tan(2015^(@)24')`.

Answer

To find the value of \( \tan(2015^\circ 24') \) using trigonometric tables, we can follow these steps:

### Step 1: Convert Minutes to Decimal Degrees
First, we need to convert the angle from degrees and minutes to decimal degrees.

1 degree = 60 minutes, so:
\[ 24' = \frac{24}{60} = 0.4^\circ \]

Thus, we can express \( 2015^\circ 24' \) as:
\[ 2015^\circ + 0.4^\circ = 2015.4^\circ \]

### Step 2: Reduce the Angle
Since the tangent function is periodic with a period of \( 180^\circ \), we can reduce \( 2015.4^\circ \) to an equivalent angle within the range of \( 0^\circ \) to \( 180^\circ \).

To do this, we divide \( 2015.4 \) by \( 180 \):
\[ 2015.4 \div 180 \approx 11.208 \]
Taking the integer part, we have \( 11 \), which means:
\[ 2015.4^\circ - 11 \times 180^\circ = 2015.4^\circ - 1980^\circ = 35.4^\circ \]

### Step 3: Find the Tangent Value
Now, we need to find \( \tan(35.4^\circ \) using the trigonometric tables.

From the trigonometric tables, we can find:
\[ \tan(35.4^\circ) \approx 0.711 \]

### Final Answer
Thus, the value of \( \tan(2015^\circ 24') \) is approximately:
\[ \tan(2015^\circ 24') \approx 0.711 \]

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