Given the triangle with sides \( a = 15 \), \( b = 11 \), and angle \( C \) as a right angle, we want to find \( \cos B \).
In a right triangle, we can use the cosine definition:
\[ \cos B = \frac{\text{adjacent side}}{\text{hypotenuse}} \]
Here, side \( a \) (15) is opposite angle \( B \), and side \( b \) (11) is adjacent to angle \( B \). To find the hypotenuse \( c \), we use the Pythagorean theorem:
\[ c^2 = a^2 + b^2 \] \[ c^2 = 15^2 + 11^2 \] \[ c^2 = 225 + 121 \] \[ c^2 = 346 \] \[ c = \sqrt{346} \]
Now, we can find \( \cos B \):
\[ \cos B = \frac{b}{c} = \frac{11}{\sqrt{346}} \]
Thus, the value of \( \cos B \) exactly is:
\[ \cos B = \frac{11}{\sqrt{346}} \]
Therefore, the correct response is:
Start Fraction 11 over Start Root 346 End Root End Fraction.
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