If `tan theta=(1)/sqrt(5)` and `theta` lies in the first quadrant, the value of `cos theta` is :

Options

A. Energy
B. Force
C. Specific heat
D. Latent heat

Explanation

To find the value of \( \cos \theta \) given that \( \tan \theta = \frac{1}{\sqrt{5}} \) and \( \theta \) lies in the first quadrant, we can follow these steps:

### Step 1: Understand the relationship of tangent in a right triangle
The tangent of an angle in a right triangle is defined as the ratio of the length of the opposite side (perpendicular) to the length of the adjacent side (base). Therefore, we can express this as:
\[ \tan \theta = \frac{\text{opposite}}{\text{adjacent}} = \frac{1}{\sqrt{5}} \]

### Step 2: Assign values to the sides of the triangle
For simplicity, let's assign the length of the opposite side (perpendicular) as \( 1 \) and the length of the adjacent side (base) as \( \sqrt{5} \). Thus, we have:
- Opposite side = \( 1 \)
- Adjacent side = \( \sqrt{5} \)

### Step 3: Use the Pythagorean theorem to find the hypotenuse
According to the Pythagorean theorem, the hypotenuse \( h \) can be calculated as:
\[ h = \sqrt{(\text{opposite})^2 + (\text{adjacent})^2} = \sqrt{1^2 + (\sqrt{5})^2} \]
Calculating this gives:
\[ h = \sqrt{1 + 5} = \sqrt{6} \]

### Step 4: Calculate \( \cos \theta \)
The cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse:
\[ \cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{\sqrt{5}}{\sqrt{6}} \]

### Final Answer
Thus, the value of \( \cos \theta \) is:
\[ \cos \theta = \frac{\sqrt{5}}{\sqrt{6}} \]