Question

determine the value of z. round your answer to the nearest tenth. * 1 point
triangle image with right angle, one leg 4.5, angle 40° at the top, sides z (horizontal leg), y (hypotenuse)
your answer

Explanation:

Step1: Identify trigonometric ratio

For the $40^\circ$ angle, the side of length 4.5 is the opposite side, and $z$ is the adjacent side. Use the tangent ratio:
$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

Step2: Substitute known values

$\tan(40^\circ) = \frac{4.5}{z}$

Step3: Rearrange to solve for z

$z = \frac{4.5}{\tan(40^\circ)}$

Step4: Calculate the value

Using $\tan(40^\circ) \approx 0.8391$,
$z \approx \frac{4.5}{0.8391} \approx 5.4$

Answer:

5.4