Things to remember about 30-60-90 triangle

The 30-60-90 Triangle is a special type of a right triangle. The three angles of these triangles are , and . The lengths of the sides of these types of triangles are always in the ratio of .

It’s a good idea to memorize the ratio:  as it can help you save some precious time in the test.

Example:

If the length of the largest side of a right triangle is 10 inches and one of the angles is 60°, what is the length (in inches) of the smallest side?

A) 

B) 

C) 

D) 

E) 

Solution:

Step 1: We have been given two angles of this triangle. Since this is a right triangle one of the angles must be 90°. We are told that one of the angles is 60°, therefore the third angle must be:

180 – 90 – 60 = 30°

Hurray, we are dealing with a special 30-60-90 triangle!

Step 2: We also know that the lengths of the sides of this type of triangles are always in the ratio of . We also know that the largest side measures   inches. If  is the measure of the smallest side, if follows that 

C is the correct answer.