If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content
Current time:0:00Total duration:3:43

Right triangle geometry — Harder example

Video transcript

- [Voiceover] It is given that the sine of 58 degrees is equal to 0.8480, cosine of 58 degrees is 0.5299, and actually, they're just giving us the first few digits of these, they keep going on and on and on, and tangent of 58 degrees is 1.600. In the figure above, angle VWY, V, W, Y, and WZV, are right angles, they've already labelled them as right angles. What is the length of segment VY to the nearest integer? So VY, VY is the hypotenuse of this big triangle right over here, and what else do we know about that big triangle? We know the angle, 58 degrees, and we know the length of VW. We could view this as the adjacent side, to this angle. So we know the angle, we know the adjacent side. We know the adjacent side, and we're trying to figure out the hypotenuse. So which trig function deals with adjacent and hypotenuse? Well, we could go to the soh-cah-toa definition of our trig functions. Soh-cah-toa. Sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent. So we're dealing with the adjacent, which we know, and we need to figure out what the hypotenuse is. So we're gonna deal with the adjacent and the hypotenuse, so we should think about using cosine. So the cosine of 58 degrees, is going to be equal to the length of the adjacent side, to that angle, 5.3 divided by the length of the hypotenuse, and that's actually what we care about, that's the length of segment VY, which we could just write V, Y, without writing the line above it, this means the length of VY. So now we could just solve for VY, so if you multiply, or actually why don't I just, instead of having to write VY over and over again, let's just call this whole thing H, H for hypotenuse. So this whole thing, right over here, that is equal to H. Let's see, if you multiply both sides by H, you're gonna get H times the cosine of 58 degrees, is equal to 5.3. Then you could divide both sides by the cosine of 58 degrees, and you get H is equal to 5.3 divided by the cosine of 58 degrees, and they tell us what the cosine of 58 degrees is, it's 0.5299. So this is going to be equal to 5.3 divided by 0.5299, it actually keeps going, and we need to figure out what this is to the nearest integer, so definitely wanna get a calculator out for that. And so, we have 5.3 divided by, 0.5299. And I'm just gonna use the numbers they gave us, even though my calculator has a cosine function, that probably would have given us more precision, but I'm gonna make sure we're using the same numbers here, so this is gonna be equal to, well, rounded to the nearest integer, well, even to the nearest hundredth, this is gonna be equal to 10. So this is the length of this side over here, is going to be equal to 10. Now if any of this that I just did looked like Greek to you, and you are not Greek, I encourage you to watch the basic trigonometry videos on Khan Academy. This is an interesting problem, because this was a pretty straightforward application of the definition of cosine, and they just confuse you a little bit, by drawing this other right triangle here.