yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Using right triangle ratios to approximate angle measure | High school geometry | Khan Academy


2m read
·Nov 10, 2024

We're told here are the approximate ratios for angle measures: 25 degrees, 35 degrees, and 45 degrees.

So, what they're saying here is if you were to take the adjacent leg length over the hypotenuse leg length for a 25-degree angle, it would be a ratio of approximately 0.91. For a 35-degree angle, it would be a ratio of 0.82. And then they do this for 45 degrees and they do the different ratios right over here.

So, we're going to use the table to approximate the measure of angle D in the triangle below. So pause this video and see if you can figure that out.

All right, now let's work through this together. Now, what information do they give us about angle D in this triangle? Well, we are given the opposite length right over here. Let me label that: that is the opposite leg length, which is 3.4.

And we're also given, what is this right over here? Is this adjacent or is this a hypotenuse? You might be tempted to say, well, this is right next to the angle, or this is one of the lines, or it's on the ray that helps form the angle. So maybe it's adjacent. But remember, adjacent is the adjacent side that is not the hypotenuse, and this is clearly the hypotenuse.

It is the longest side; it is the side opposite the 90-degree angle. So this right over here is the hypotenuse.

So, we're given the opposite leg length and the hypotenuse length, and so let's see which of these ratios deal with the opposite and the hypotenuse.

And if we, let's see, this first one is adjacent and hypotenuse. The second one here is hypotenuse—sorry, opposite and hypotenuse. So that's exactly what we're talking about; we're talking about the opposite leg length over the hypotenuse length.

So, in this case, what is going to be our opposite leg length over our hypotenuse leg length? It's going to be 3.4 over 8. Three point four over eight, which is approximately going to be equal to... let me do this down here.

This is eight goes into three point four. Eight doesn't go into three. Eight goes into 34 four times. Four times eight is 32. If I subtract, and I could scroll down a little bit, I get a two. I can bring down a zero. Eight goes into 20 two times, and that's about as much precision as any of these have.

And so it looks like for this particular triangle and this angle of the triangle, if I were to take a ratio of the opposite length and the hypotenuse length, opposite over hypotenuse, I get 0.42. So that looks like this situation right over here.

So that would imply that this is a 25-degree angle—approximately.

More Articles

View All
Missing Dial Trailer | National Geographic
You don’t know heartbreak until you’re running through the jungle, yelling for your son’s name. “Roben! Oh, that’s my son, chip off the old block!” He emailed us right before he headed into the jungle. “It should be difficult to get lost forever.” What t…
Horizontal area between curves | Applications of definite integrals | AP Calculus AB | Khan Academy
So I have two curves graphed here, and we’re used to seeing things where Y is a function of X. But here we have X as a function of Y. In fact, we can write this top expression as being a function of Y, and this second one, just to make it different, we co…
The Space Race | Meet Ed Dwight | National Geographic Documentary Films
My hope was just getting into space in any kind of way, but they were not gonna let that happen. And they said, number one, I wasn’t tall enough. I was Catholic. I wasn’t Black enough. I was not the model of the Negro race. I was a one-man operation when …
The Odds of Existence
In life, anything is possible because we can never fully understand how the world works. The laws of physics prevent us from being able to tell the future. Everything we predict is a probability; some are a lot more probable, others are less probable, whi…
What The U.S. Need to Do?
And you’ve studied how empires rise and how empires fall over the past several hundred years. You’ve said that generally speaking, empires collapsed for three main reasons. The first is debt, the second is internal conflict—so you know, polarity within a …
Spooked in the Woods | Port Protection
The woods in the middle of nowhere you would think would be a quiet, peaceful little place. However, when the weather is crummy, it can be a very loud, mysterious, nerve-wracking area. Not only mysterious but dangerous. Here in the dense rainforest, winds…