Questions: Solve for x. Round to the nearest hundredth.

Solution Steps

We are given a right triangle with the adjacent side to angle \(x\) as 3 cm and the hypotenuse as 5 cm.

We can use the cosine ratio, which relates the adjacent side and the hypotenuse to the angle. \[\cos(x) = \frac{\text{adjacent}}{\text{hypotenuse}}\]

Substituting the given values into the cosine ratio, we get: \[\cos(x) = \frac{3}{5}\]

To find \(x\), we need to take the inverse cosine (arccos) of both sides: \[x = \arccos\left(\frac{3}{5}\right)\] Using a calculator, we get: \[x \approx 53.13^\circ\]

Final Answer The final answer is $\boxed{53.13}$