Question

when solving for x, the sine of 33° is used. what other angle and trigonometric function could be used to solve for x? a. cos 57° b. tan 33° c. tan 57° d. cos 33°

Explanation:

Step1: Recall angle - sum property of right - triangle

In a right - triangle, if one non - right angle is $33^{\circ}$, the other non - right angle is $90^{\circ}-33^{\circ}=57^{\circ}$ because the sum of the interior angles of a triangle is $180^{\circ}$ and one angle is $90^{\circ}$.

Step2: Recall trigonometric co - function relationships

We know that $\sin\theta=\cos(90^{\circ}-\theta)$. Given $\sin33^{\circ}$ is used to solve for $x$. Since $33^{\circ}$ and $57^{\circ}$ are complementary angles ($33 + 57=90$), $\sin33^{\circ}=\cos57^{\circ}$.

Answer:

A. $\cos57^{\circ}$