Question

in the right triangle, one leg is 30, one acute angle is 20°, and we need to find the length of the other leg w (the leg opposite the 20° angle or adjacent? wait, the right angle is at the bottom left, the horizontal leg is 30, the vertical leg is w, and the acute angle at the bottom right is 20°).

Explanation:

Step1: Identify trigonometric ratio

We use the tangent function, since we know the adjacent side to the 20° angle (30) and need the opposite side \(W\). The tangent of an angle is $\frac{\text{opposite}}{\text{adjacent}}$.
$\tan(20^\circ) = \frac{W}{30}$

Step2: Solve for \(W\)

Rearrange the formula to isolate \(W\) by multiplying both sides by 30.
$W = 30 \times \tan(20^\circ)$

Step3: Calculate the value

Use $\tan(20^\circ) \approx 0.3640$ to compute \(W\).
$W \approx 30 \times 0.3640 = 10.92$

Answer:

$W \approx 10.92$