Answer :
To find the angle [tex]\( A \)[/tex] in degrees when [tex]\(\tan(A) = \frac{5}{7}\)[/tex], follow these steps:
1. Understand the Problem: We need to find an angle [tex]\( A \)[/tex] such that the tangent of the angle is the fraction [tex]\(\frac{5}{7}\)[/tex].
2. Use Inverse Tangent Function: To find the angle, we use the inverse tangent function, often written as [tex]\(\arctan\)[/tex] or [tex]\(\tan^{-1}\)[/tex]. This function gives us the angle whose tangent is a given number. So, we calculate [tex]\( A = \tan^{-1}\left(\frac{5}{7}\right) \)[/tex].
3. Convert the Angle to Degrees: The inverse tangent function typically returns the angle in radians. To convert this to degrees, we use the conversion factor: [tex]\(1 \text{ radian} = 57.2958 \text{ degrees}\)[/tex].
4. Calculate the Angle in Degrees: After calculating [tex]\( \tan^{-1}\left(\frac{5}{7}\right) \)[/tex], you convert the result from radians to degrees to get approximately 35.5 degrees.
5. Round to the Nearest Tenth: The angle, when rounded to the nearest tenth of a degree, is 35.5 degrees.
Thus, the angle [tex]\( A \)[/tex] that satisfies the condition [tex]\(\tan(A) = \frac{5}{7}\)[/tex] is approximately 35.5 degrees. The closest answer choice is 35.5 degrees, which confirms that our calculations are correct.
1. Understand the Problem: We need to find an angle [tex]\( A \)[/tex] such that the tangent of the angle is the fraction [tex]\(\frac{5}{7}\)[/tex].
2. Use Inverse Tangent Function: To find the angle, we use the inverse tangent function, often written as [tex]\(\arctan\)[/tex] or [tex]\(\tan^{-1}\)[/tex]. This function gives us the angle whose tangent is a given number. So, we calculate [tex]\( A = \tan^{-1}\left(\frac{5}{7}\right) \)[/tex].
3. Convert the Angle to Degrees: The inverse tangent function typically returns the angle in radians. To convert this to degrees, we use the conversion factor: [tex]\(1 \text{ radian} = 57.2958 \text{ degrees}\)[/tex].
4. Calculate the Angle in Degrees: After calculating [tex]\( \tan^{-1}\left(\frac{5}{7}\right) \)[/tex], you convert the result from radians to degrees to get approximately 35.5 degrees.
5. Round to the Nearest Tenth: The angle, when rounded to the nearest tenth of a degree, is 35.5 degrees.
Thus, the angle [tex]\( A \)[/tex] that satisfies the condition [tex]\(\tan(A) = \frac{5}{7}\)[/tex] is approximately 35.5 degrees. The closest answer choice is 35.5 degrees, which confirms that our calculations are correct.
