In $\triangle ABC, \angle B= 90°$. if $\frac{AB}{AC} = \frac{1}{2}$, then $cos$ $C$ is equal to

In $\triangle ABC, \angle B= 90°$. if $\frac{AB}{AC} = \frac{1}{2}$, then $cos$ $C$ is equal to

In $\triangle ABC$, given that $\angle B = 90^\circ$, and

$ \displaystyle \frac{AB}{AC} = \frac{1}{2} $,

we need to find $\cos C$.

### Step 1: Define Trigonometric Ratio
By definition,

$ \displaystyle \cos C = \frac{\text{adjacent side}}{\text{hypotenuse}} = \frac{AB}{AC} $

### Step 2: Substitute Given Values
Since we are given

$ \displaystyle \frac{AB}{AC} = \frac{1}{2} $,

it follows that:

$ \displaystyle \cos C = \frac{1}{2} $.

### Final Answer:
$ \cos C = \frac{1}{2} $.