Question

find the tangent of ∠t. simplify your answer and write it as a proper fraction. tan(t) =

Explanation:

Step1: Recall tangent - ratio formula

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$ for an acute angle $\theta$. For $\angle T$, the side opposite $\angle T$ is $VU$ and the side adjacent to $\angle T$ is $TU$.

Step2: Use the Pythagorean theorem to find $VU$

By the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 13$ (hypotenuse) and $b = 5$ (one leg). Let $a$ be the other leg $VU$. Then $a=\sqrt{13^{2}-5^{2}}=\sqrt{169 - 25}=\sqrt{144}=12$.

Step3: Calculate $\tan(T)$

$\tan(T)=\frac{VU}{TU}$. Since $VU = 12$ and $TU = 5$, $\tan(T)=\frac{12}{5}$.

Answer:

$\frac{12}{5}$