Question

express cos h as a fraction in simplest terms.

Explanation:

Step1: Find the length of \( GH \) using Pythagorean theorem

In right - triangle \( VGH \), by Pythagorean theorem \( a^{2}+b^{2}=c^{2} \), where \( c = VH=26 \), \( a = VG = 24 \), and \( b=GH \).

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Step2: Use the cosine formula

The cosine of an angle in a right - triangle is defined as \( \cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}} \). For \( \angle H \), the adjacent side is \( GH \) and the hypotenuse is \( VH \).

$$ \cos H=\frac{GH}{VH} $$

Substitute \( GH = 10 \) and \( VH=26 \)

$$ \cos H=\frac{10}{26}=\frac{5}{13} $$

Answer:

\(\frac{5}{13}\)