Calculating angles with sine, cosine, and tangent

The length of the hypotenuse and the other two sides can be determined using the triangle’s angles and the sine, cosine, and tangent operations. The sides of a right-angled triangle, apart from the hypotenuse, can be labeled as Opposite and Adjacent based on their positions in the triangle relative to the relevant angle, as shown in Figure 8.8:

Figure 8.8: The adjacent and opposite triangle sides for

Note that for these rules, either angle can be used. If the angle at the other end of the hypotenuse (other than what is shown in Figure 8.8) is used, then the labels for Opposite and Adjacent change positions.

The relationship between the sides and hypotenuse that represent the trigonometric function of sine is as follows:

The relationship for the trigonometric function of cosine is as follows:

The relationship for the trigonometric function of tangent is as follows:

Working with...