Question

question
express \\( \cos f \\) as a fraction in simplest
terms.
answer
attempt 1 out of 3
\\( \cos f = \\)
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Explanation:

Step1: Recall the cosine formula

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. For angle $F$, the adjacent side to angle $F$ is $FG$ (we need to find $FG$ using the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 35$ (hypotenuse) and $b = 21$ (one leg)). Let $a=FG$. Then $FG=\sqrt{35^{2}-21^{2}}=\sqrt{(35 + 21)(35 - 21)}=\sqrt{56\times14}=\sqrt{784}=28$.

Step2: Calculate $\cos F$

Using the cosine formula $\cos F=\frac{\text{adjacent}}{\text{hypotenuse}}$. The adjacent side to angle $F$ is $FG = 28$ and the hypotenuse $FH=35$. So $\cos F=\frac{28}{35}=\frac{4}{5}$.

Answer:

$\frac{4}{5}$