Find the inclination of the line whose slope is :
`0.7646`

Answer

To find the inclination of the line whose slope is \(0.7646\), we can follow these steps:

### Step 1: Understand the relationship between slope and inclination
The slope of a line is defined as the tangent of the angle of inclination (\(\theta\)) of that line with respect to the positive x-axis. This can be expressed as:
\[ \text{slope} = \tan(\theta) \]

### Step 2: Set up the equation
Given that the slope is \(0.7646\), we can write:
\[ \tan(\theta) = 0.7646 \]

### Step 3: Use the inverse tangent function
To find the angle \(\theta\), we take the inverse tangent (also known as arctan) of the slope:
\[ \theta = \tan^{-1}(0.7646) \]

### Step 4: Calculate the angle
Using a calculator or trigonometric tables, we find:
\[ \theta \approx 37.24^\circ \]

### Step 5: Finalize the answer
Thus, the inclination of the line is approximately:
\[ \theta \approx 37^\circ 24' \]

### Summary of the solution
The inclination of the line whose slope is \(0.7646\) is \(37^\circ 24'\).

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