Question

start at the \start\ box and w
x
38°
15
start
19.0
x
18.7
13.9

Explanation:

Step1: Identify the trigonometric ratio

We have a right triangle with adjacent side \( 15 \) and angle \( 38^\circ \), and we need to find the hypotenuse \( x \). The cosine function relates the adjacent side and the hypotenuse: \( \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \).

Step2: Set up the equation

Using the cosine formula, \( \cos(38^\circ) = \frac{15}{x} \).

Step3: Solve for \( x \)

Rearrange the equation to \( x = \frac{15}{\cos(38^\circ)} \). Calculate \( \cos(38^\circ) \approx 0.7880 \), then \( x = \frac{15}{0.7880} \approx 19.0 \). Wait, but let's check again. Wait, maybe I misread. Wait, the adjacent side is 15, angle 38 degrees. Wait, no, maybe the adjacent is 15, and we can also check with the other value. Wait, the arrow shows 19.0. Wait, let's recalculate. \( \cos(38^\circ) \approx 0.788 \), so \( x = 15 / \cos(38^\circ) \approx 15 / 0.788 \approx 19.0 \). So that matches the 19.0 arrow. So the value of \( x \) is approximately 19.0.

Answer:

\( \boxed{19.0} \)