In this lesson, we will learn how to solve right triangles. A right triangle has one angle that measures exactly 90 degrees. We can find unknown sides and angles using trigonometric ratios like sine, cosine, and tangent.
The three basic trigonometric ratios help us relate angles to side lengths. Sine equals opposite over hypotenuse. Cosine equals adjacent over hypotenuse. Tangent equals opposite over adjacent. These ratios are the foundation for solving right triangles.
Let's solve a practical example. Given angle A equals 30 degrees and the hypotenuse c equals 10, we can find the unknown sides. Using sine of 30 degrees equals a over 10, we get a equals 5. Using cosine of 30 degrees equals b over 10, we get b equals 8.66.
Now let's find an unknown angle. Given sides a equals 3, b equals 4, and c equals 5, we can find angle A. Using sine A equals a over c, we get sine A equals 0.6. Taking the inverse sine, angle A equals 36.87 degrees. We can verify this is correct since angle B equals 90 minus 36.87, which is 53.13 degrees.