30-60-90 Triangle: Theorem, Properties & Formula


Choose an answer and hit 'next'. You will receive your score and answers at the end.

question 1 of 3

You are given the length of the side which is across from a 60 degree angle in a right triangle. To find the length of the other two sides you must first

Create Your Account To Take This Quiz

As a member, you'll also get unlimited access to over 79,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Try it risk-free
Try it risk-free for 30 days. Cancel anytime
Already registered? Log in here for access

1. Find the value of x in the triangle pictured below.

2. Find the length of the shorter leg in the triangle pictured below.

Create your account to access this entire worksheet
A Premium account gives you access to all lesson, practice exams, quizzes & worksheets
Access to all video lessons
Quizzes, practice exams & worksheets
Certificate of Completion
Access to instructors
Create an account to get started Create Account

About This Quiz & Worksheet

Triangles that have 30, 60, and 90 degree angles have specific and unique characteristics. This interactive quiz will use multiple choice questions, including practice problems, to test your knowledge of the dimensions, angles, and equations involved in 30-60-90 triangles.

Quiz & Worksheet Goals

Use these assessment tools to assess your knowledge of:

  • How to calculate the length of a leg or hypotenuse
  • How to determine the degree of an angle
  • The equations involved in solving for a triangle's missing dimensions
  • The relationships between side lengths and angles of 30-60-90 triangles

Skills Practiced

This worksheet and quiz let you practice the following skills:

  • Problem solving - use acquired knowledge to solve for missing angles and side lengths of 30-60-90 triangles
  • Interpreting information - verify that you can read information regarding the geometric equations of triangles and interpret them correctly
  • Information recall - access the knowledge you've gained regarding the equations and rules for 30-60-90 triangles

Additional Learning

To learn more about this facet of geometry, review the corresponding lesson on 30-60-90 triangles. This lesson covers the following topics:

  • Right triangles
  • Hypotenuses
  • How to solve for missing angles and side lengths
  • Rationalizing denominators