How To Solve 30-60-90 Triangle Problems

When it comes to logical problems in mathematics, geometry comes first and 30-60-90 triangles usually have a major role to play in any question that you might encounter. Which means you have to understand these basics to perform exceptional well in this aspect of mathematics.

Are you finding it difficult to understand these triangles and their respective applications? Right here, we will be taking you through these angles one after the other and showing you how they are derived, explain the ratipa that exist between each of these sides, and how they are solved.

What is 30-60-90 triangles all about?

Basically, 30-60-90 triangles are angles within a scalene right angle triangle. These angles have a ratio of 1:2:\sqrt3, with 1 represents 30° which is the opposite angle, 2 representing the 60° which is the hypotenuse angle, and sqrt3 representing the 90° which is also the adjacent angle.

By imputing variables into the ratio, it becomes x:2x:x\sqrt3. Using the relationship that exists between these ratios, you will be able to find a missing angle or side given the value of the two other sides and a angle.

Another way to use this 30-60-90 triangles is to put in the general Pythagorean theorem. With this, you can also calculate the values of a side in a triangle given other sides of the same right angle triangle.

How is 30-60-90 triangles solved?

Solving any mathematical problem related to 30-60-90 triangles can be easy if you understand the basics and you know how to apply them the right way and at the right time. Let’s take for example, you are given the value of a leg across from 30° “5” which can also be referred to as the opposite side and you are requested to solve the values of the two other sides. All you have to do is recall the 30-60-90 triangles formula which was shared ealier which is  x:2x:x\sqrt3 and apply it.

From our formula, we can find the value of our two other sides just by inputing the given value into the equation. Where x is equals 5, the hypotenuse(2x) becomes 2 \times 5 = 10, while the adjacent side becomes x\sqrt{3} = 5 \sqrt{3}.

To aid comprehension, let’s solve another example. In case where you are given the value of hypotenuse which is 4 to solve for the value of the two other sides, what you have to do again is to use your  30-60-90 triangles formula.

Using the same procedure above, 4 = 2x. After which it is factorize, the value of x becomes 2, while the value of the other side becomes 2 \sqrt{3}.

Knowing your 30-60-90 triangles will help you do well on the SAT. The triangles are provided on the reference table, but being familiar with them will help you do better. Knowing them should be part of your SAT prep.