Now based on all of that, let's address the elephant The corresponding third side in the other triangle, that these are completelyĬongruent triangles. Well, then that means that the third side is going to be congruent to Two sides of those triangles that are congruent toĮach other, and we do, we have this side isĬongruent to that side and we have this side is ofĬourse congruent to itself. In two different triangles, and you have a sideīetween two of those angles that is congruent, and you have Have three angles like this that all have the same measure So we know that this angle is going to be, it's going to have the same Have two angles in common, in a triangle, in twoĬorresponding triangles, then the third angle is This angle is 90 degrees, that this angle has toīe 90 degrees as well, because they have to add up to 180. Isosceles triangle like this, where these two sides are equivalent, then the base angles are going to have the same measure as well. This expression on the right, let me figure out what else What is the value of sine of angle CBD minus cosine of angle BAC? Pause this video and see It doesn't matter if it's at the bottom of the triangle or not - in fact, you could rotate the triangle in the video 90 degrees counterclockwise and get something that looks exactly the same as the image you provided.ĪBC above, AB is equal to BC, so this is equal to that. In the video, Sal calls the perpendicular of the triangle the adjacent angle since it's the side that touches the angle he's interested in. If the image was talking about angle B, then the base of the triangle becomes the opposite side instead of the adjacent one (since it doesn't touch angle B). Notice how the adjacent side touches angle A, and the opposite side doesn't touch angle A. In the image you provided, the sides that are labeled adjacent and opposite are labeled that way relative to angle A. In reality, the side that is "adjacent" is relative to the angle you want to find the cosine of. In fact, in a pure visual sense, the base of the triangle is kind of arbitrary, since we can rotate the triangle to make either of the two legs of the triangle the base. We can divide 78 by 5 to clear the fraction and get the decimal 15."Adjacent side" doesn't always mean the base of the triangle. We need a Common Denominator of 5, so we multiply 13/1 (13 as a fraction) by 5: Since we're trying to find AC, we add 13 + 13/5. So we'll take sides DE corresponding to BE, because we have the measure of both. "Next, we'll set up proportions to solve for the length of EC." That means take two corresponding sides of each triangle and set them equal to each other, and one of those sides will be the one we're trying to find, which is EC. "Then, you'll need to recognize that the smaller triangle is similar" to the bigger triangle and "△AED is similar to △CEB" Okay, not too bad. Square Root of both sides (to clear the x^2) makes 13 = x (Because sq rt of 169 = 13)Īlso, you could remember that 5-12-13 is a common Pythagorean Triple.Īnyway, that makes the Hypotenuse of the big triangle AE = 13. Oh man - that's a heck of a question! Okay let's see.Īlright so "Since we're dealing with right triangles, you'll need to use the Pythagorean theorem to figure out the missing side length of the big triangle".
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