find cd. write your answer as an integer or as a decimal rounded to the nearest tenth. cd =

Explanation:

Step1: Use tangent function

In right - triangle $BCD$, $\tan\theta=\frac{opposite}{adjacent}$. Here, $\theta = 40^{\circ}$, the adjacent side to $\angle B$ is $BC = 6$, and the opposite side is $CD$. So, $\tan B=\tan40^{\circ}=\frac{CD}{BC}$.

Step2: Solve for $CD$

Since $BC = 6$ and $\tan40^{\circ}\approx0.839$, we have $CD = BC\times\tan40^{\circ}$. Substituting the value of $BC$, we get $CD=6\times0.839 = 5.034$.

Step3: Round the result

Rounding $5.034$ to the nearest tenth gives $5.0$.

Answer:

$5.0$