Question

find the length of side w.
36.5 cm
43.6 cm
18.0 cm
21.4 cm
(the right triangle has an angle of 40°, hypotenuse of 28 cm, and the side to find is marked as w)

Explanation:

Step1: Identify trigonometric ratio

We use the sine function: $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$, where $\theta=40^\circ$, opposite side is $w$, hypotenuse is 28 cm.

Step2: Rearrange to solve for $w$

$w = 28 \times \sin(40^\circ)$

Step3: Calculate the value

$\sin(40^\circ) \approx 0.6428$, so $w \approx 28 \times 0.6428 = 18.0$

Answer:

18.0 cm