Answer :
To solve for [tex]\( x \)[/tex] when [tex]\(\tan x = \frac{3}{4}\)[/tex], you need to find the angle [tex]\( x \)[/tex] whose tangent is [tex]\(\frac{3}{4}\)[/tex]. The steps to find [tex]\( x \)[/tex] are as follows:
1. Understand the Tangent Function: The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side. Here, we have [tex]\(\tan x = \frac{3}{4}\)[/tex], which means the opposite side is 3 units and the adjacent side is 4 units.
2. Use the Inverse Tangent Function: To find the angle [tex]\( x \)[/tex], you need to use the inverse tangent function, often denoted as [tex]\(\tan^{-1}\)[/tex] or [tex]\(\arctan\)[/tex]. This function gives you the angle whose tangent is the given value.
3. Calculate the Angle in Degrees: Using a calculator or a trigonometric table, calculate [tex]\(\tan^{-1}\left(\frac{3}{4}\right)\)[/tex] to find the angle in degrees.
4. Round the Result: Once you have the angle, round it to the nearest tenth to get the answer.
After performing these steps, you find that:
- The angle [tex]\( x \)[/tex] whose tangent is [tex]\(\frac{3}{4}\)[/tex] is approximately [tex]\( 36.9 \)[/tex] degrees when rounded to the nearest tenth.
Therefore, the solution is [tex]\( x = 36.9 \)[/tex] degrees.
1. Understand the Tangent Function: The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side. Here, we have [tex]\(\tan x = \frac{3}{4}\)[/tex], which means the opposite side is 3 units and the adjacent side is 4 units.
2. Use the Inverse Tangent Function: To find the angle [tex]\( x \)[/tex], you need to use the inverse tangent function, often denoted as [tex]\(\tan^{-1}\)[/tex] or [tex]\(\arctan\)[/tex]. This function gives you the angle whose tangent is the given value.
3. Calculate the Angle in Degrees: Using a calculator or a trigonometric table, calculate [tex]\(\tan^{-1}\left(\frac{3}{4}\right)\)[/tex] to find the angle in degrees.
4. Round the Result: Once you have the angle, round it to the nearest tenth to get the answer.
After performing these steps, you find that:
- The angle [tex]\( x \)[/tex] whose tangent is [tex]\(\frac{3}{4}\)[/tex] is approximately [tex]\( 36.9 \)[/tex] degrees when rounded to the nearest tenth.
Therefore, the solution is [tex]\( x = 36.9 \)[/tex] degrees.
