Finding missing lengths in slope triangles
About this video
Sal finds a missing side E in two similar slope triangles. Because corresponding sides have the same ratio, the medium sides 4 and 6 show a multiplier of 1.5, so E = 3 x 1.5 = 4.5. He checks with a second method, using the ratio within each triangle: E/6 = 3/4, giving E = 4.5 again.
You'll be able to
- find the scale factor between similar triangles from a pair of corresponding sides.
- use the scale factor to find a missing side length.
- set up an equation using ratios within triangles to find a missing side.
Key words
- similar triangles
- Triangles with the same shape, whose corresponding sides are in the same ratio.
- corresponding sides
- Sides that match up in the same position in the two triangles.
- ratio
- A comparison of two numbers by division.
- hypotenuse
- The longest side of a right triangle, opposite the right angle.
Transcript
- [Instructor] So let's assume that these two triangles are similar. And based on that, we want to figure out what E is going to be equal to. And we have to be careful using E as an unknown because some of you will learn that E, like pi, can represent a very special number in mathematics.
So typically when you see a lowercase E like this, it represents that number. But for the sake of this video, let's just assume that it represents an unknown. Well, when you're dealing with similar triangles, the ratio of corresponding sides is going to be the same.
So for example, if we take the medium side on both of these, the longest is this right over here. Some people might call that the hypotonus. Some people might call, well, that's on the line, so you can kind of see the slope of the line there. But the medium side is this one.
It's the second longest side. This one and this one. Those are the two that correspond to each other. Now, when you go from the smaller triangle to the larger one, when you go from four to six, what are we doing? We are multiplying. And you want to think about multiplying.
And you want to think about ratios and division, not addition or subtraction. We're multiplying to go from four to six, you multiply by 1.5. So we could do the same thing on the shorter side, because E is the length of the shorter side on that larger triangle.
So if you go from three to E, we also need to multiply by 1.5. Three times 1.5 is equal to 4.5. And we are then done. Now, there's other ways that we could have tackled this. We could have looked at the ratios within each of these triangles, say, the ratio of the short side to the medium side.
So we could have said that E over, I'll maintain the colors, E over six is equal to, is equal to the short side here, which is three over the medium side here, which is four. And a little bit of algebra right over here, if you multiply both sides by six, multiply both sides by six, you are going to get that E is equal to three-fourths of six, which is the same thing as 0.75 times six.
Or you could view that as 18 divided by four, which is the same thing as nine divided by two, which is 4.5. And we get the exact same result.
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