## Right Triangle Trigonometry

Right triangle trigonometry is a branch of mathematics that deals with the calculation of angles and sides of a triangle. It is based on the Pythagorean theorem, which states that the sum of the squares of the sides of a right triangle must equal the square of the hypotenuse. In 4.2 right triangle trigonometry, you will learn how to use this theorem to solve for angles and sides of right triangles.

## Angles, Sides, and Ratios

Right triangle trigonometry utilizes the angles and sides of a right triangle to calculate the ratios between them. The most important ratios are sine, cosine, and tangent. Sine (sin) is the ratio of the opposite side over the hypotenuse, cosine (cos) is the ratio of the adjacent side over the hypotenuse, and tangent (tan) is the ratio of the opposite side over the adjacent side.

## Solving for Angles

When solving for angles, you will use the ratios defined above. By knowing the lengths of two sides of a triangle, you can calculate the angle opposite of them by using the inverse functions of sine, cosine, and tangent. You can also use the Pythagorean theorem to solve for the hypotenuse and then use the ratios to calculate the angles.

## Solving for Sides

When solving for sides, you will use the ratios and the angles. By knowing two angles and the length of one side, you can calculate the lengths of the other two sides. You can also use the Pythagorean theorem to solve for the hypotenuse and then use the ratios to calculate the lengths of the other two sides.

## Conclusion

4.2 right triangle trigonometry is a great way to understand how to use the Pythagorean theorem and the ratios of sine, cosine, and tangent to solve for angles and sides in right triangles. With the right tools and knowledge, you can easily solve for the angles and sides of any right triangle.

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