Questions: Solve for x. Round your answer to the nearest tenth.

Solution Steps

We are given a right triangle with one leg having a length of 42 and an angle of 64 degrees. We are asked to find the length of the hypotenuse, denoted by \(x\).

Since we are given the adjacent side and need to find the hypotenuse, we can use the cosine function. Recall that \(\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}\). In our case, \(\theta = 64^\circ\), adjacent side = 42, and hypotenuse = \(x\).

We have \(\cos(64^\circ) = \frac{42}{x}\).

To solve for \(x\), we can multiply both sides of the equation by \(x\) and then divide by \(\cos(64^\circ)\): \(x = \frac{42}{\cos(64^\circ)}\)

Using a calculator, we find that \(\cos(64^\circ) \approx 0.4384\). Therefore, \(x \approx \frac{42}{0.4384} \approx 95.80\)

Final Answer