Question

(07.01 MC)Look at the figure:If tan xº = 3/y and cos xº= y/z , what is the value of sin xº? (1 point)

Answer 1

The trigonometric ratios are defined as follows:

Let "θ" represent the angle of interest, then the ratios are:

$\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypothenuse}} \\ \cos \theta=\frac{adjacent}{hypothenuse} \\ \tan \theta=\frac{opposite}{adjacent} \end{gathered}$

We know that the tangent of xº is equal to the ratio 3/y, the numerator is the opposite side to the angle xº and the denominator is the adjacent side of the angle.

$\tan xº=\frac{3\to\text{opposite}}{y\to\text{adjacent}}$

The cosine of xº is equal to the ratio y/z, where the numerator is the adjacent side to the angle xº, and the denominator is the hypothenuse of the triangle.

$\cos xº=\frac{y\to\text{adjacent}}{z\to\text{hypothenuse}}$

So, the sides of the right triangle, with respect of angle xº are:

opposite= 3

adjacent= y

hypothenuse= z

The sine of xº is defined as the ratio between the opposite side to the angle and the hypothenuse, you can express it as follows:

$\sin xº=\frac{3}{z}$