Answered

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In right triangle \(XYZ\), \(\angle X\) and \(\angle Z\) are complementary angles, and \(\cos(X)\) is \(\frac{9}{11}\). What is \(\sin(Z)\)?

A. \(\frac{9}{11}\)

B. \(\frac{11}{9}\)

C. \(\frac{\sqrt{20}}{11}\)

D. [tex]\(\frac{\sqrt{20}}{9}\)[/tex]

Sagot :

GinnyAnswer
To solve this problem, let's first recall that in a right triangle, the two non-right angles are complementary. This means that if one of those angles is \( \angle X \), the other angle, \( \angle Z \), satisfies the equation:

[tex]\[ \angle X + \angle Z = 90^\circ \][/tex]

Given this complementary relationship, we know that:

[tex]\[ \sin(Z) = \cos(X) \][/tex]

Now, we are given that:

[tex]\[ \cos(X) = \frac{9}{11} \][/tex]

Since \( \sin(Z) \) is equal to \( \cos(X) \) for complementary angles, we can directly write:

[tex]\[ \sin(Z) = \frac{9}{11} \][/tex]

Therefore, the correct value of \( \sin(Z) \) is:

[tex]\[ \boxed{\frac{9}{11}} \][/tex]

The correct choice is A.
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