Answer :
To solve for [tex]\( x \)[/tex] where [tex]\(\tan x = \frac{3}{4}\)[/tex], you want to find the angle [tex]\( x \)[/tex] in degrees.
Let's go through the steps:
1. Use the Inverse Tangent Function:
- To find [tex]\( x \)[/tex], you use the inverse tangent function, often written as [tex]\(\tan^{-1}\)[/tex] or [tex]\(\arctan\)[/tex]. So you'll calculate [tex]\( x = \arctan\left(\frac{3}{4}\right) \)[/tex].
2. Convert from Radians to Degrees:
- The value you get from [tex]\(\arctan\)[/tex] will be in radians. To convert radians to degrees, use the formula:
[tex]\[
\text{Degrees} = \text{Radians} \times \frac{180}{\pi}
\][/tex]
3. Round to the Nearest Tenth:
- After converting to degrees, round your answer to the nearest tenth.
Following these steps, you will find that the angle [tex]\( x \)[/tex] is approximately [tex]\( 36.9^\circ \)[/tex].
Therefore, the correct answer is [tex]\(\boxed{36.9}\)[/tex].
Let's go through the steps:
1. Use the Inverse Tangent Function:
- To find [tex]\( x \)[/tex], you use the inverse tangent function, often written as [tex]\(\tan^{-1}\)[/tex] or [tex]\(\arctan\)[/tex]. So you'll calculate [tex]\( x = \arctan\left(\frac{3}{4}\right) \)[/tex].
2. Convert from Radians to Degrees:
- The value you get from [tex]\(\arctan\)[/tex] will be in radians. To convert radians to degrees, use the formula:
[tex]\[
\text{Degrees} = \text{Radians} \times \frac{180}{\pi}
\][/tex]
3. Round to the Nearest Tenth:
- After converting to degrees, round your answer to the nearest tenth.
Following these steps, you will find that the angle [tex]\( x \)[/tex] is approximately [tex]\( 36.9^\circ \)[/tex].
Therefore, the correct answer is [tex]\(\boxed{36.9}\)[/tex].