What are your chances of acceptance?

Duke University

Loading…

UCLA

Loading…

Unweighted GPA:** 3.7**

1.0

4.0

SAT: **720 math**

200

800

| **800 verbal**

200

800

Low accuracy (4 of 18 factors)

Can someone help me with 30-60-90 triangles? I know I should remember this from geometry class, but I'm a little confused. What's the most efficient way to solve them?

5 months ago

When working with 30-60-90 triangles, it's important to recognize the ratios between the side lengths. The ratios, based on the angles of the triangle, are as follows:

1. The side opposite the 30-degree angle is the shortest side, and we'll call it x.

2. The side opposite the 60-degree angle is √3 times longer than the side opposite the 30-degree angle, so its length will be x√3.

3. The side opposite the 90-degree angle (the hypotenuse) is twice the length of the side opposite the 30-degree angle, so its length will be 2x.

Given one side length of a 30-60-90 triangle, you can easily find the other two sides using these ratios.

Here's an example to illustrate the process:

Suppose you have a 30-60-90 triangle with a hypotenuse length of 10. Using the ratios above, you can find the other two side lengths:

1. Since the hypotenuse is 2x, and it has a length of 10, then x = 10/2 = 5. This gives us the side length opposite the 30-degree angle, which is 5.

2. To find the side length opposite the 60-degree angle, multiply x by √3: 5√3.

Now you have all the side lengths: the side opposite 30 degrees is 5, the side opposite 60 degrees is 5√3, and the side opposite 90 degrees (the hypotenuse) is 10.

Remembering these ratios and applying them accordingly is the most efficient way to solve 30-60-90 triangles.

5 months ago

CollegeVine’s Q&A seeks to offer informed perspectives on commonly asked admissions questions. Every answer is refined and validated by our team of admissions experts to ensure it resonates with trusted knowledge in the field.