Answer:

Topic: The Six Trigonometric Ratios

Three things I've learned:

1. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot).

2. These ratios are used to relate the angles of a right triangle to the lengths of its sides.

3. Each ratio has a specific formula and represents the relationship between certain sides of a right triangle.

Two things that interest me:

1. I find it fascinating how these ratios can be used to solve real-world problems involving angles and distances, such as in navigation, engineering, and physics.

2. The trigonometric ratios have connections to circular functions and can be visualized using the unit circle, which adds depth and complexity to their applications.

One application of what I've learned:

One application of the trigonometric ratios is in surveying and land measurement. By using trigonometry, surveyors can determine distances, heights, and angles with great accuracy. For example, they can use the tangent ratio to calculate the height of a building by measuring the distance from the building and the angle of elevation. This knowledge helps in constructing accurate maps, designing infrastructure, and planning urban development.