Question

find the value of tan e rounded to the nearest hundredth, if necessary.
answer attempt 1 out of 2
tan e =

Explanation:

Step1: Recall the tangent ratio formula

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For angle $E$, the side opposite to angle $E$ is $CD = 7$, and the side adjacent to angle $E$ is $DE=\sqrt{30}$.

Step2: Calculate $\tan E$

$\tan E=\frac{CD}{DE}=\frac{7}{\sqrt{30}}$. Rationalize the denominator: $\frac{7}{\sqrt{30}}\times\frac{\sqrt{30}}{\sqrt{30}}=\frac{7\sqrt{30}}{30}\approx\frac{7\times5.477}{30}$.
$7\times5.477 = 38.339$, then $\frac{38.339}{30}\approx1.28$.

Answer:

$1.28$