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Answer :
To find the angle [tex]\( A \)[/tex] in degrees when [tex]\(\tan(A) = \frac{5}{7}\)[/tex], you can use the inverse tangent function, often written as [tex]\(\tan^{-1}\)[/tex] or [tex]\(\text{arctan}\)[/tex].
Here's how you can solve it step-by-step:
1. Use the Inverse Tangent Function:
- First, calculate the angle [tex]\( A \)[/tex] in radians by finding the inverse tangent of [tex]\(\frac{5}{7}\)[/tex]. This is done using the [tex]\(\text{arctan}\)[/tex] function:
[tex]\[
A = \tan^{-1}\left(\frac{5}{7}\right)
\][/tex]
2. Convert Radians to Degrees:
- Angles can be measured in radians or degrees. Since the options for the answer are in degrees, you'll need to convert the result from radians to degrees.
- Use the conversion factor: [tex]\(1 \text{ radian} = \frac{180}{\pi} \text{ degrees}\)[/tex].
3. Rounding:
- After converting to degrees, you'll round your result to the nearest tenth of a degree for precision.
4. Calculation Result:
- Following these steps gives you the value of [tex]\( A \approx 35.5\)[/tex] degrees.
Therefore, the angle [tex]\( A \)[/tex] is approximately 35.5 degrees.
Here's how you can solve it step-by-step:
1. Use the Inverse Tangent Function:
- First, calculate the angle [tex]\( A \)[/tex] in radians by finding the inverse tangent of [tex]\(\frac{5}{7}\)[/tex]. This is done using the [tex]\(\text{arctan}\)[/tex] function:
[tex]\[
A = \tan^{-1}\left(\frac{5}{7}\right)
\][/tex]
2. Convert Radians to Degrees:
- Angles can be measured in radians or degrees. Since the options for the answer are in degrees, you'll need to convert the result from radians to degrees.
- Use the conversion factor: [tex]\(1 \text{ radian} = \frac{180}{\pi} \text{ degrees}\)[/tex].
3. Rounding:
- After converting to degrees, you'll round your result to the nearest tenth of a degree for precision.
4. Calculation Result:
- Following these steps gives you the value of [tex]\( A \approx 35.5\)[/tex] degrees.
Therefore, the angle [tex]\( A \)[/tex] is approximately 35.5 degrees.
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