Question

score on last try: 0 of 1 pts. see details for more. you can retry this question below find the value of x. (figure is not to scale.) triangle with right angle, side 44, angle 66°, hypotenuse x x = input box calculator interface enter a mathematical expression more.. find the value of x. (figure is not to scale.)

Explanation:

Step1: Identify trigonometric ratio

In the right triangle, we have the adjacent side to the \(66^\circ\) angle as \(44\) and the hypotenuse as \(x\). The cosine function relates adjacent and hypotenuse: \(\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}\).
So, \(\cos(66^\circ)=\frac{44}{x}\).

Step2: Solve for \(x\)

Rearrange the formula to solve for \(x\): \(x = \frac{44}{\cos(66^\circ)}\).
Calculate \(\cos(66^\circ)\approx0.4067\), then \(x=\frac{44}{0.4067}\approx108.2\) (or keep it as \(\frac{44}{\cos(66^\circ)}\) for exact form).

Answer:

\(\frac{44}{\cos(66^\circ)}\) (or approximately \(108.2\))