Question

Solve for x. Round to the nearest tenth ofa degree, if necessary.5.3HGto8.5F

Answer 1

We have a rigth triangle, where we have to find the measure of x.

We can use trigonometric ratios to relate the lengths of the sides and the measure of x.

The lengths we know are from the hypotenuse and the adyacent side of x, so we can use the following trigonometric ratio:

`\begin{gathered} \cos (x)=\frac{\text{Adyacent}}{\text{Hypotenuse}} \\ \cos (x)=(5.3)/(8.5) \\ x=\arccos ((5.3)/(8.5))\approx\arccos (0.623)\approx51.4\degree \end{gathered}`

Answer: x = 51.4°