Question

question find the value of tan u rounded to the nearest hundredth, if necessary.

Explanation:

Step1: Recall tangent - ratio formula

The tangent of an angle in a right - triangle is defined as $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For angle $U$ in right - triangle $TUE$, the side opposite to angle $U$ is $TE$ and the side adjacent to angle $U$ is $TU$.

Step2: Identify the lengths of opposite and adjacent sides

From the right - triangle, the length of the side opposite to angle $U$ (i.e., $TE$) is $3$, and the length of the side adjacent to angle $U$ (i.e., $TU$) is $2$.

Step3: Calculate the value of $\tan U$

Using the formula $\tan U=\frac{\text{opposite}}{\text{adjacent}}$, we have $\tan U=\frac{3}{2}=1.50$.

Answer:

$1.50$