Question

express cos h as a fraction in simplest terms.

Explanation:

Step1: Recall cosine - ratio in right - triangle

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. For $\angle H$, the adjacent side to $\angle H$ is $GH$ and the hypotenuse is $FH$.

Step2: Identify side lengths

We know that $FH = 26$ and we need to find $GH$. Using the Pythagorean theorem in right - triangle $FGH$: $FH^{2}=FG^{2}+GH^{2}$. Given $FG = 24$ and $FH = 26$, we can solve for $GH$.
\[

$$\begin{align*} GH&=\sqrt{FH^{2}-FG^{2}}\\ &=\sqrt{26^{2}-24^{2}}\\ &=\sqrt{(26 + 24)(26 - 24)}\\ &=\sqrt{50\times2}\\ &=\sqrt{100}\\ & = 10 \end{align*}$$

\]

Step3: Calculate $\cos H$

Now, $\cos H=\frac{GH}{FH}$. Substituting $GH = 10$ and $FH = 26$, we get $\cos H=\frac{10}{26}=\frac{5}{13}$.

Answer:

$\frac{5}{13}$