Question

solve for x. round to the nearest tenth, if necessary. triangle tuv with right angle at u, angle at t is 40 degrees, side tu is 64, side tv is x

Explanation:

Step1: Identify trigonometric ratio

We use cosine: $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$
Here, $\theta=40^\circ$, adjacent side $=64$, hypotenuse $=x$.

Step2: Rearrange to solve for $x$

$x = \frac{64}{\cos(40^\circ)}$

Step3: Calculate value

First, $\cos(40^\circ) \approx 0.7660$, so $x \approx \frac{64}{0.7660} \approx 83.55$

Step4: Round to nearest tenth

$x \approx 83.6$

Answer:

$83.6$