Answer:
The length of AB is 48 centimeters.
Step-by-step explanation:
According to the given information, AC is the hypotenuse of the right triangle, since it is opposed to a right angle (angle B). BC is the leg adjacent to angle B, whereas AB is the leg opposed to angle C. Then, we can find the length of AB by the following trigonometric identity:
[tex]\sin C = \frac{AB}{AC}[/tex] (1)
If we know that [tex]AC = 96\,cm[/tex] and [tex]C = 30^{\circ}[/tex], then the length of [tex]AB[/tex] is:
[tex]AB = AC\cdot \sin C[/tex]
[tex]AB = (96\,cm) \cdot \sin 30^{\circ}[/tex]
[tex]AB = 48\,cm[/tex]
The length of AB is 48 centimeters.
