30 60 90 Triangle Rules Math

Geometry proper understanding of 30 60 90 triangles will allow you to solve geometry questions that would either be impossible to solve without knowing your ratio rules or at the very least would take.

30 60 90 triangle rules math. The most frequently studied right triangles the special right triangles are the 30 60 90 triangles followed by the 45 45 90 triangles. Find the missing side of the given triangle. Scroll down the page for more examples and solutions on how to use. Notice that these ratios hold for all 30 60 90 triangles regardless of the actual length of the sides.

This free geometry lesson introduces the subject and provides examples for calculating the lengths of sides of a triangle. Remembering the rules for 30 60 90 triangles will help you to shortcut your way through a variety of math problems. In the study of trigonometry the 30 60 90 triangle is considered a special triangle knowing the ratio of the sides of a 30 60 90 triangle allows us to find the exact values of the three trigonometric functions sine cosine and tangent for the angles 30 and 60. The most important rule to remember is that this special right triangle has one right angle and its sides are in an easy to remember consistent relationship with one another the ratio is a.

For example sin 30 read as the sine of 30 degrees is the ratio of the side opposite the. As stated previously a right triangle is any triangle that has at least one right angle 90 degrees. The lengths of the sides of a 30 60 90 triangle are in the ratio of 1 3 2. Thus it is called a 30 60 90 triangle where smaller angle will be 30.

So for any triangle whose sides lie in the ratio 1 3 2 it will be a 30 60 90 triangle without exception. The hypotenuse is the longest side in a right triangle which is different from the long leg. The 30 60 90 right triangle is a special case triangle with angles measuring 30 60 and 90 degrees. 30 60 90 triangle in trigonometry.

And because this is a 30 60 90 triangle and we were told that the shortest side is 8 the hypotenuse must be 16 and the missing side must be 8 3 or 8 3. The following diagram shows a 30 60 90 triangle and the ratio of the sides. Example of 30 60 90 rule. The 30 60 90 triangle is one example of a special right triangle.

Knowing your 30 60 90 triangle rules will be able to save you time and energy on a multitude of different math problems namely a wide variety of geometry and trigonometry problems. 30 60 90 triangle rules and properties. Our final answer is 8 3. As it is a right triangle in which the hypotenuse is the double of one of the sides of the triangle.

Although all right triangles have special features trigonometric functions and the pythagorean theorem.