Question

simplify your answer and write it as a proper fraction, improper fraction, or whole number.
tan(h) =

Explanation:

Step1: Recall tangent - ratio definition

In a right - triangle, $\tan(H)=\frac{\text{opposite}}{\text{adjacent}}$. For angle $H$, the opposite side to angle $H$ is side $GI$ and the adjacent side is side $GH$. First, find side $GH$ using the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 26$ (hypotenuse) and $b = 24$ (one of the legs). Let the other leg be $a$. Then $a=\sqrt{c^{2}-b^{2}}$.

Step2: Calculate side $GH$

$a=\sqrt{26^{2}-24^{2}}=\sqrt{(26 + 24)(26 - 24)}=\sqrt{50\times2}=\sqrt{100}=10$.

Step3: Calculate $\tan(H)$

$\tan(H)=\frac{GI}{GH}$. Since $GI = 24$ and $GH = 10$, then $\tan(H)=\frac{24}{10}=\frac{12}{5}$.

Answer:

$\frac{12}{5}$