Question

in right triangle xyz, ∠x and ∠z are complementary angles and cos(x) is \\(\frac{9}{11}\\). what is sin(z)?

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

b. \\(\frac{sqrt{20}}{9}\\)

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

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

Explanation:

Step1: Recall complementary angle identity

For complementary angles $∠X + ∠Z = 90^\circ$, $\sin(Z) = \cos(X)$.

Step2: Substitute given value

$\cos(X) = \frac{9}{11}$, so $\sin(Z) = \frac{9}{11}$.

Answer:

A. $\frac{9}{11}$