Question

solve for x. round to the nearest tenth, if necessary. triangle image with right angle at v, side vw labeled x, hypotenuse wu labeled 2.6, angle at w is 36°

Explanation:

Step1: Identify adjacent side, hypotenuse

Angle $W=36^\circ$, hypotenuse $WU=2.6$, adjacent side $VW=x$.

Step2: Use cosine definition

$\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$
$\cos(36^\circ)=\frac{x}{2.6}$

Step3: Solve for x

$x=2.6\times\cos(36^\circ)$
Calculate $\cos(36^\circ)\approx0.8090$, so $x\approx2.6\times0.8090\approx2.1034$

Step4: Round to nearest tenth

$x\approx2.1$

Answer:

$2.1$