Final answer:
By utilizing the ratios from a special 30°-60°-90° right triangle and knowing one side, the other two sides were found to be 10 inches and 10√3 inches, with the original 20-inch side opposite the 60° angle. Keep in mind that your calculator can be in degree mode or radian mode. Be sure you can toggle back and forth so that you are always in the appropriate units for each problem.
Step-by-step explanation:
The student is asked to find the exact measures of the other two sides of a triangle with one angle measuring 30° and one side measuring 20 inches. Working with special right triangles, specifically the 30°-60°-90° triangle, we can use the ratio of sides which is 1:√3:2. Since the 20-inch side is opposite the 60° angle (the lengthiest side in this special triangle), we can deduce that the side opposite the 30° angle (the shortest side) is 10 inches (20 inches / 2), and using Pythagoras' theorem or the special triangle ratios, the side opposite the 90° angle (the hypotenuse) must be √3 times longer than the shortest side, which is 10√3 inches (approximately 17.32 inches).
There are three types of special right triangles. 30-60-90 triangles have side ratios of. 45-45-90 triangles have side ratios of. Pythagorean triple triangles have integer side lengths and include examples such as (3, 4, 5), (5, 12, 13), and (7, 24, 25).
Trigonometry is the study of triangles. If you know the angles of a triangle and one side length, you can use the properties of similar triangles and proportions to completely solve for the missing sides.