Answer:
[tex]\sf A = \boxed{45}^\circ [/tex]
Step-by-step explanation:
Given:
- Adjacent side [tex]\sf AC = 38 [/tex] m
- Hypotenuse [tex]\sf AB = 54 [/tex] m
Using the definition of cosine:
[tex]\sf \cos(A) = \dfrac{Adjacent}{Hypotenuse} [/tex]
[tex]\sf \cos(A) = \dfrac{AC}{AB} [/tex]
Substituting the values:
[tex]\sf \cos(A) = \dfrac{38}{54} [/tex]
Now, to find the measure of angle [tex]\sf A [/tex], take the inverse cosine (arccos) of [tex]\sf \dfrac{38}{54} [/tex]:
[tex]\sf A = \cos^{-1} \left(\dfrac{38}{54}\right) [/tex]
[tex]\sf A = 45.275086845066 [/tex]
[tex]\sf A = 45^\circ \textsf{ (in nearest whole number)}[/tex]
Therefore, the answer is:
[tex]\sf A = \boxed{45}^\circ [/tex]
