Find the measure of the side of the right triangle whose length is designated by a lowercase letter. Round answers to the nearest whole number.(FIGURE CANNOT COPY)...

Find the missing side lengths in each triangle. Give the exact answer and then an approximation to two decimal places when appropriate. (TRIANGLE CAN'T COPY)

Okay, so we have a dirty 60 90 triangle. So what does it mean? Well, this means that our 30 angle your degree angle, the opposite of this is our smarter, smaller or a shorter leg. And we know that the length of our longer leg is the square roots of the times. My shorter leg, which is five. So we actually have this is five square root three. Okay. And then our high Pontius. This is twice as long as a shorter leg. So that's equal to two times I shorter languages five. And that's equal to 10.

Okay, so we know that the opposite of our dirty degree angle is are shorter length. So this is our longer leg. And this is our high Pontius. Do we know that, um are longer? Leg is equal to the square root or three times a shorter. So are along the leg. It's 40 for 123 shorter leg. So that means are shorter. Leg is equal to 40 divided by the square root of three, and it's equal to X. Now. We also want to find out how apartments. But we called up the high Panis is just two times that shortly. And that's equal to two times the fault way. So that people to 80 over a square with three. Yeah, so we get the following solutions.

All right, We're given a right triangle. Can we've got our sides being 15 and 20 and then we're trying to find to see we can. Then you should Pythagorean theorem a squared plus B squared equals C squared in order to find are missing side See So first we can put our A and which would be 15 or 20. But we're gonna make it 15 in this case. So we've got 15 meters squared, plus our view which is 20 three squared. That's in meters as well. And then we've got our C square so we can square these numbers. You're gonna be left with 225 meters plus 400 meters being equal to R C squared. There we can add those two numbers together, leaving us with 625 meters equal to C squared. Let me want to get seed by itself. So we're gonna take the square root of book side which will leave us with C being equal to 25 meters

All right, We're still talking, right? Triangles here. If we have a right triangle that looks like this sort of with 12 on one side, six on another, and then our high pot news. We don't know you. We can then use our Pythagorean theorem a squared plus B squared people c squared in order to find that high partners see, so we can use either six or 12 for a all you six six squared, most 12 squared. Fill those in being equal to R C squared. We can then multiply these numbers by themselves to swear them. So we've got 36 plus 144 being equal to C squared. So then we can add are 36 in 1 44 together, giving us 180 being equal to C squared. And then our last step is going to be to take the square root of both sides in order to isolate, See, so we'll take the square root square root. From there, we are given C is equal to 13.416 We went around this to the nearest 10th. So we're going to rewrite our 13 now. We're looking at this 10th place right here. So are for you. Look to the right of it. If this number right here is five or higher, you're going around that for up. Otherwise, it's going to stays before it's a one riches lower, so it's going to be just for so are, so it'll be 13.