In this lesson, we will learn how to solve right triangles. A right triangle has one angle that measures exactly 90 degrees. We label the vertices as A, B, and C, where B is the right angle. The sides are labeled as a, b, and c, where c is the hypotenuse opposite to the right angle.
The three basic trigonometric ratios help us solve right triangles. Sine of angle A equals the opposite side divided by the hypotenuse. Cosine of angle A equals the adjacent side divided by the hypotenuse. Tangent of angle A equals the opposite side divided by the adjacent side. These ratios are fundamental tools in trigonometry.
Let's solve a practical example. Given angle A equals 30 degrees and the hypotenuse c equals 10, we need to find the unknown sides a and b. 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. This demonstrates how trigonometric ratios help us find missing sides.
Now let's find an unknown angle. Given that the opposite side a equals 6 and the hypotenuse c equals 10, we can find angle A. Since sine A equals a over c, we have sine A equals 0.6. Using the inverse sine function, angle A equals 36.87 degrees. We can verify this by checking that angle C equals 90 minus 36.87, which is 53.13 degrees.