Question

find the exact value of cos b in simplest radical form.

Explanation:

Step1: Recall cosine - ratio in right - triangle

In right - triangle $\triangle BCD$ with right - angle at $C$, the cosine of an acute angle $B$ is defined as $\cos B=\frac{\text{adjacent}}{\text{hypotenuse}}$.

Step2: Identify adjacent and hypotenuse sides

The side adjacent to angle $B$ is $BC = \sqrt{66}$, and the hypotenuse is $BD=11$.

Step3: Calculate $\cos B$

$\cos B=\frac{\sqrt{66}}{11}=\frac{\sqrt{6\times11}}{11}=\frac{\sqrt{6}\times\sqrt{11}}{11}=\frac{\sqrt{6}}{\sqrt{11}}=\frac{\sqrt{6}\times\sqrt{11}}{11}=\frac{\sqrt{66}}{11}$

Answer:

$\frac{\sqrt{66}}{11}$