Razones Trigonométricas | Hallar un lado | Ejemplo 1

Understanding Trigonometric Ratios in Right Triangles

Introduction to Trigonometric Ratios

• The video introduces the application of trigonometric ratios, starting with a simple exercise to find the value of a side in a right triangle.

• It emphasizes that this is the first application video and will cover basic concepts thoroughly for clarity.

Characteristics of Right Triangles

• A right triangle must have one angle measuring 90 degrees; trigonometric ratios apply only in such triangles.

• The sides are identified: two legs (catetos) forming the right angle and the hypotenuse, which is the longest side.

Identifying Triangle Sides

• The closest leg to an angle is called the adjacent leg, while the opposite leg is further away from that angle. This distinction is crucial for applying trigonometric functions.

Known Values and Required Calculation

• In this example, known values include a hypotenuse measuring 10 meters and an angle (theta) of 32 degrees; we aim to find the length of the opposite leg (x).

• It's important to write down all known data clearly before proceeding with calculations.

Selecting Appropriate Formula

• To solve for x, we need a formula involving both the hypotenuse and opposite leg; thus, sine function (sin) is selected since it relates these two sides directly.

Solving for x Using Sine Function

• The equation set up is sin(32°) = x / 10m; rearranging gives us x = 10m * sin(32°). This step involves isolating x on one side of the equation.

Calculator Usage and Final Calculation

• Ensure your calculator is set to degree mode before performing calculations; results should be interpreted correctly based on local conventions regarding decimal points (e.g., using periods instead of commas).

• After calculation, it’s found that x ≈ 5.3 meters, indicating how long this side measures in relation to other triangle dimensions.

Practice Exercise

Understanding Trigonometric Ratios

Introduction to Trigonometric Functions

• The discussion begins with the relationship between the hypotenuse and the adjacent side in a right triangle, emphasizing that the cosine function is used for this calculation.

• The formula presented is: Cosine of 65 degrees equals the adjacent side divided by the hypotenuse, which measures 13 meters.

• A calculator is suggested for finding values, with an approximation provided (either 54 or 549), depending on desired accuracy.

Tangent Function Explanation

• The tangent function is introduced as it relates to both opposite and adjacent sides of a right triangle.

• The formula for tangent is stated: Tangent of an angle equals the opposite side (x) over the adjacent side (7).

Conclusion and Further Learning