Question

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

Explanation:

Step1: Recall tangent ratio formula

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For $\angle V$ in right - triangle $TUV$, the opposite side to $\angle V$ is $TU = 28$ and the adjacent side to $\angle V$ is $UV$. First, find $UV$ using the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = TV = 35$ and $a = TU = 28$. Let $UV=b$, then $b=\sqrt{TV^{2}-TU^{2}}$.
$UV=\sqrt{35^{2}-28^{2}}=\sqrt{(35 + 28)(35 - 28)}=\sqrt{63\times7}=\sqrt{441}=21$.

Step2: Calculate $\tan V$

$\tan V=\frac{TU}{UV}$. Substitute $TU = 28$ and $UV = 21$ into the formula. $\tan V=\frac{28}{21}=\frac{4}{3}\approx1.33$.

Answer:

$1.33$