Trigonometry is an important mathematical concept that is used to study relationships between angles and sides of triangles. In Unit 8 Homework 4 of a trigonometry class, students are required to solve for a missing side or angle of a triangle, given the lengths of other sides or angles. In order to solve these types of problems, students must understand the trigonometric ratios, which are the ratios of two sides of a right triangle.

## The Three Trigonometric Ratios

The three trigonometric ratios are sine, cosine, and tangent. These ratios are always the same within a right triangle, regardless of the size of the triangle. They can be used to find the unknown side of a triangle when the other two sides are known. The sine ratio is equal to opposite side divided by hypotenuse, or sin (A) = opposite side/hypotenuse. The cosine ratio is equal to adjacent side divided by hypotenuse, or cos (A) = adjacent side/hypotenuse. Finally, the tangent ratio is equal to the opposite side divided by adjacent side, or tan (A) = opposite side/adjacent side.

## Using Trigonometric Ratios to Find Missing Sides

Once students understand the trigonometric ratios, they can use them to find the length of a missing side. To do so, they must first identify the angle and the sides that are known. Then, they need to use the appropriate ratio to solve for the missing side. For example, if the angle is 30 degrees and the opposite side is 5, then the hypotenuse can be found by using the sine ratio: sin (30) = 5/hypotenuse. Therefore, the hypotenuse is equal to 10.

## Finding Missing Angles

In addition to finding the length of a missing side, students can also use trigonometric ratios to find the measure of a missing angle. To do so, they must first determine the known sides and then use the appropriate ratio to solve for the missing angle. For example, if the hypotenuse is 10 and the adjacent side is 6, then the angle can be found using the cosine ratio: cos (A) = 6/10. Therefore, the angle is equal to 53.13 degrees.

Unit 8 Homework 4 of a trigonometry class requires students to solve for a missing side or angle of a triangle, given the lengths of other sides or angles. In order to do so, students must understand the three trigonometric ratios, which are the ratios of two sides of a right triangle. Once students understand these ratios, they can use them to solve for the length of a missing side or the measure of a missing angle.