Answer:
[tex]x = 23.6[/tex]
Step-by-step explanation:
To find the missing side of a right-angled triangle, first look at the given angle, and notice its relationships with the given and required sides.
In this case:
• The side adjacent to the given 38° angle is [tex]x[/tex] (required).
• The hypotenuse is 30 units.
The trigonometric ratio that relates the adjacent side and hypotenuse of a triangle is cosine (cos), where:
[tex]\boxed{cos \space\ \theta = \frac{adjacent}{hypotenuse}}[/tex].
Substituting into the formula:
[tex]cos (38^{\circ}) = \frac{x}{30}[/tex]
⇒ [tex]x = cos(38^{\circ}) \times 30[/tex]
⇒ [tex]x = 23.6[/tex]
