Question

which equations is equivalent to $sin(27)=\frac{8}{x}$
$cos(63)=\frac{8}{x}$
$cos(63)=\frac{x}{8}$
$sin(27)=\frac{x}{8}$
$sin(63)=\frac{x}{8}$

Explanation:

Step1: Use co-function identity

Recall $\sin(\theta) = \cos(90^\circ - \theta)$
For $\theta=27^\circ$, $90^\circ-27^\circ=63^\circ$, so $\sin(27^\circ)=\cos(63^\circ)$

Step2: Substitute into original equation

Original equation: $\sin(27^\circ)=\frac{8}{x}$
Substitute $\sin(27^\circ)=\cos(63^\circ)$: $\cos(63^\circ)=\frac{8}{x}$

Answer:

A. $\cos(63)=\frac{8}{x}$