8.1.2 Trigonometric Ratios
Key Objectives • Find the sine, cosine, and tangent of an acute angle. • Use trigonometric ratios to find side lengths in right triangles and to solve real-world problems. Key Terms • A trigonometric ratio is a ratio of two sides of a right triangle.
• The sine of an angle is the ratio of the length of the leg opposite the angle to the length of the hypotenuse. • The cosine of an angle is the ratio of the length of the leg adjacent to the angle to the length of the hypotenuse. • The tangent of an angle is the ratio of the length of the leg opposite the angle to the length of the leg adjacent to the angle. Example 1 Finding Trigonometric Ratios
The sine of an angle is the ratio of the length of the leg opposite the angle to the length of the hypotenuse. The cosine of an angle is the ratio of the length of the leg adjacent to the angle to the length of the hypotenuse. The tangent of an angle is the ratio of the length of the leg opposite the angle to the length of the leg adjacent to the angle. Three trigonometric ratios for angles in a 3-4-5 right triangle are written in this example. Sin A is the length of the opposite leg to ∠ A over the length of the hypotenuse of the triangle, or 3/5 = 0.6. Cos A is the length of the adjacent leg to ∠ A over the length of the hypotenuse of the triangle, or 4/5 = 0.8. Tan B is the length of the opposite leg to ∠ B over the length of the adjacent leg, or 4/3 ≈ 1.33.
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