Question

given \\(\delta def\\), which is not equal to \\(\cos(f)\\)?

\\(\sin(f)\\)

\\(\sin(d)\\)

\\(\cos(d)\\)

\\(\tan(f)\\)

Explanation:

Identify the given triangle properties

We are given a right isosceles triangle \(\triangle DEF\) with:

• Right angle at vertex \(E\) (\(\angle E = 90^\circ\))
• Side lengths \(DE = 5\) and \(EF = 5\)
• Hypotenuse \(DF = 5\sqrt{2}\)

Calculate the target trigonometric ratio

Using the Cosine Ratio knowledge point

$$ \cos(F) = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{EF}{DF} = \frac{5}{5\sqrt{2}} = \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2} $$

Evaluate each option ratio

Using the Trigonometric Ratios knowledge point

$$
LATEXBLOCK0
$$

Determine the non-equal ratio

Comparing the calculated values:

• \(\cos(F) = \frac{\sqrt{2}}{2}\)
• \(\tan(F) = 1

eq \frac{\sqrt{2}}{2}\)

Answer:

• (A) \(\sin (F)\)
• (B) \(\sin (D)\)
• (C) \(\cos (D)\)
• (D) \(\tan (F)\) (Correct answer)