Question

find the value of tan v rounded to the nearest hundredth, if necessary. t 28 35 u v

Explanation:

Step1: Recall tangent formula

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For $\angle V$, the opposite side to $\angle V$ is $TU = 28$ and we first need to find the adjacent side $UV$ using the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 35$ and $a = 28$. Let $UV=b$, then $b=\sqrt{c^{2}-a^{2}}$.

Step2: Calculate the adjacent side

$UV=\sqrt{35^{2}-28^{2}}=\sqrt{(35 + 28)(35 - 28)}=\sqrt{63\times7}=\sqrt{441}=21$.

Step3: Calculate $\tan V$

$\tan V=\frac{TU}{UV}=\frac{28}{21}=\frac{4}{3}\approx1.33$.

Answer:

$1.33$