Welcome to trigonometry! Trigonometry is the branch of mathematics that studies the relationships between the sides and angles of triangles. The word trigonometry comes from Greek, where trigonon means triangle and metron means measure. So trigonometry literally means triangle measurement.
In a right triangle, we identify three important components. The hypotenuse is the longest side, opposite to the right angle. The adjacent side is the side next to our angle of interest. The opposite side is across from our angle. These three sides form the foundation for all trigonometric relationships.
The three basic trigonometric ratios are sine, cosine, and tangent. Sine is the ratio of the opposite side to the hypotenuse. Cosine is the ratio of the adjacent side to the hypotenuse. Tangent is the ratio of the opposite side to the adjacent side. These ratios allow us to find unknown sides and angles in right triangles.
Let's solve a practical problem. We want to find the height of a building. We know the distance from the building is 50 meters, and the angle of elevation is 30 degrees. Using the tangent ratio, tangent of 30 degrees equals height divided by 50. Therefore, height equals 50 times tangent of 30 degrees, which is approximately 28.9 meters.
To summarize what we've learned about trigonometry: It's the study of triangle relationships, focusing on three main ratios. Sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, and tangent equals opposite over adjacent. These fundamental concepts allow us to solve many real-world problems involving angles and distances.