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Current time:0:00Total duration:3:52

Right triangle word problems — Basic example

Video transcript

- [Instructor] A builder needs to add cross braces to a 3.5 meter by five meter opening between supports in a building, as shown in the figure above. So okay, so this is 3.5 meters high, five meters wide, and then this right over here is a cross brace. So that right over there is a cross brace. There's another one that goes that way. So which of the following is closest to the length of one of the cross braces? And they give us four options here, and so let's look at this. So closest to the length of one of the cross braces. So if you look at the cross brace that I have started to shade in here in this navy blue, you see if you look at that, and then if you look at this five-meter side. So let me do this in a brighter color. If you look at this, and then you look at this five-meter side, and then you look at this 3.5-meter side, you see that they form a right triangle. And so if we wanted to solve for the length of the cross brace, that cross brace is a hypotenuse of the right triangle. It's the longest side of that right triangle, and so we know that we can apply the Pythagorean theorem here. We know the Pythagorean theorem tells us that the length of the sum of the two shorter side squared. So five squared plus 3.5 squared is going to be equal to the length of the hypotenuse squared. So let's just call this length h, or actually, we could call it c if we're used to using the Pythagorean theorem, calling this a, b, c, and say a squared plus b squared is equal to, let's call that c, c for cross braces, is equal to c squared. Now five squared is pretty straight forward, and that's going to be 25. Now, 3.5 squared, let's see. 3.5 times 3.5, five times five is 25, three times five is 15 plus two is 17. Now, I'm gonna use the three. Three times five is 15, three times three is nine plus one is 10, five plus zero is five, seven plus five is 12, one plus one is two, and then you have one right over here, and you have two digits to the right of the decimal point. So you're gonna have two digits to the right of the decimal point right over here. So this is going to be plus 12 plus 12.25 is equal to c squared. Now, 25 plus 12.25, that's going to be 37.25 is equal to c squared, or we could say that c is equal to the square root of 37.25. Now, let's think about what this is. We know that six squared is equal to 36, and we know that seven squared is equal to 49. So c is going to between, actually let me write this down. So let's see, we know that, let me give ourself some more space. Six squared is equal to 36 and seven squared is equal to 49, and we know that c squared is equal to 37.25, which is closer to 36. It's larger than 36, but it's closer to 36 than it is to 49. So I'd approximate c would be between six and seven. It's gonna be closer to six. And so let's see, out of our options right over here, 6.1 is looking pretty good. It's definitely not gonna be 8.5. 8.5 squared is going to be greater than 64, so it's not gonna be that. 3.6 meters squared, well, that's gonna be less than 16. So 6.1's looking good. This is gonna be a little bit more than 36, which 37.25 is. It's a little bit more than 36.