Hi all!

In the 30/60/90 Quiz Q3, the solution starts with some observations.

I was able to see the TWO 3/6/9 triangles… I was able to set BD=root3x

I can’t quite grasp how CB = x/root3

Here is my work… anybody see what I am missing?

Thank you for your time and assistance! First time posting hopefully both

images load.

-B

Also my equation has a problem but it was just a clerical error… it should read

CD=BD-BC

Apologies

Look at \Delta ABC. Notice that’s a 30-60-90 triangle as well - can you use that to your advantage?

In fact, you already have, in the last triangle. Let \sqrt{3}x = t. Then can you get the relationship the question is describing?

Thank you for your reply! I’ve been working through this a little more and I’m getting closer to a full understanding but still a little shaky. I’m going to repost the question with more detail in a moment. Preciate you taking the time to help me out.

For clarity I’m going to repost the quiz question, the answer, and my work.

My question is, how do we quickly arrive at the fact that AB=x BD=Root3X and, critically BC=X/Root3

I started by separating the two triangles for clarity. Looking at them separately I see AB as being either Root3X in the smaller triangle, OR X in the larger triangle. I did choose Root3x for BD based on the larger triangle. And I failed to see how CB = X/Root3.

Would be helpful to hear someone else’s logic for choosing the variables for the equation. Equation alone took me a while to work through also, but I failed to set the equation properly in the first step.