find $x$. round your answer to the nearest tenth of a degree.\n$x = \\square^{\\circ}$

Explanation:

Step1: Identify the trigonometric relationship

In a right triangle, the tangent of an angle is the ratio of the opposite side to the adjacent side. $$\tan(x) = \frac{\text{opposite}}{\text{adjacent}}$$

Step2: Substitute the given values

The side opposite to angle $x$ is $16$ and the adjacent side is $12$. $$\tan(x) = \frac{16}{12}$$

Step3: Simplify the fraction

Divide both numerator and denominator by their greatest common divisor, which is $4$. $$\tan(x) = \frac{4}{3}$$

Step4: Solve for $x$ using the arctangent function

Apply the inverse tangent function to find the measure of the angle. $$x = \arctan\left(\frac{4}{3}\right)$$

Step5: Calculate the numerical value

Use a calculator to find the value in degrees. $$x \approx 53.1301^{\circ}$$

Step6: Round to the nearest tenth

Round the result to one decimal place as requested. $$x \approx 53.1^{\circ}$$

Answer:

$x = 53.1^{\circ}$