Chapter 1: Understanding the Challenge

This exercise revolves around angle chasing within a triangle. You are presented with a scenario where the triangle's base is bisected, accompanied by two known angles of 40 degrees and 20 degrees.

Your task is to determine the value of angle x. I encourage you to pause here, grab some paper, and work through it before reading further for the solution!

Solution

To begin, let's label the sides of the triangle for clarity.

We’ve designated an arbitrary length of 1 for each half of the triangle's base. Alternatively, you can use a general term to represent these lengths. The blue angle measures 120 degrees, derived from the triangle's angle sum property.

Next, we'll apply the sine rule to calculate the length of side a.

Having found the value of a, we can now proceed with the cosine rule to find side b. Let’s focus on the triangle that contains angle x.

To determine the angle x, we can once again utilize the sine rule!

And there you have it—our solution!

Photo by baljinnyam sumiyasuren on Unsplash

How impressive is that?

What was your thought process during this challenge? I invite you to share your insights in the comments below; I'm eager to hear from you!

Chapter 2: Engaging with Math Puzzles

Explore some of the best math puzzles available on Medium, including challenges in algebra, geometry, calculus, and number theory.

In the first video titled "Building a Level has NEVER been so EASY," you will discover effective strategies for mastering geometry challenges.

The second video, "What Happened to Easy Geometry Dash Levels?" delves into the evolution of geometry puzzles in gaming.

Thank you for taking the time to read this article! If you found it helpful, please show your appreciation by giving it a clap.

If you feel inclined, consider buying me a coffee to support my writing endeavors. Your generosity means a lot!

Happy Solving, Bella 😊