To solve the problem where [tex]\(\cos (H) = \frac{x}{y}\)[/tex], we need to identify the values of [tex]\(H\)[/tex], [tex]\(x\)[/tex], and [tex]\(y\)[/tex] that satisfy this trigonometric relationship. Let's walk through the solution step-by-step.
1. Identify [tex]\(H\)[/tex]:
- The angle [tex]\(H\)[/tex] in degrees is provided to be [tex]\(60^\circ\)[/tex].
2. Understand the trigonometric relationship:
- We're using the cosine function, which is defined as the ratio of the length of the adjacent side to the length of the hypotenuse in a right-angled triangle.
3. Choose a value for the hypotenuse [tex]\(y\)[/tex]:
- For simplicity, let's choose the hypotenuse [tex]\(y\)[/tex] to be 1.
4. Calculate [tex]\(x\)[/tex]:
- Using the definition of cosine, [tex]\(\cos(60^\circ) = \frac{x}{1}\)[/tex].
- We know that [tex]\(\cos(60^\circ) = 0.5\)[/tex].
- Therefore, [tex]\(\cos(60^\circ) = 0.5 = \frac{x}{1}\)[/tex], which implies [tex]\(x = 0.5\)[/tex].
Putting this all together:
- [tex]\(H = 60^\circ\)[/tex]
- [tex]\(x = 0.5\)[/tex]
- [tex]\(y = 1\)[/tex]
Thus, the values that satisfy [tex]\(\cos(H) = \frac{x}{y}\)[/tex] are:
[tex]\[
H = 60^\circ \\
x = 0.5 \\
y = 1
\][/tex]
These values make the statement [tex]\(\cos(60^\circ) = \frac{0.5}{1}\)[/tex] true.
