Question

determine the value of y. round your answer to the nearest tenth. *
1 point
right triangle with one leg 4.5, angle 40° opposite to that leg, hypotenuse y, another leg z
your answer

Explanation:

Step1: Identify trigonometric ratio

For the $40^\circ$ angle, the given side (4.5) is opposite, and $y$ is the hypotenuse. Use sine:
$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

Step2: Substitute known values

$\sin(40^\circ) = \frac{4.5}{y}$

Step3: Rearrange to solve for y

$y = \frac{4.5}{\sin(40^\circ)}$

Step4: Calculate the value

$\sin(40^\circ) \approx 0.6428$, so:
$y \approx \frac{4.5}{0.6428} \approx 7.0$

Answer:

7.0