Two hallways, one of width 4 feet, the other of width 7 feet, meet at a right angle. See the illustration. We want to find the length of this ladder, so we're trying to find this total length. Let's realize we could split it up into two triangles. We could have one triangle here, and let's call that hypotenuse A. We could have a second triangle here, and let's call this hypotenuse B. So the whole length of the ladder would be A+B. So when we look up here, we know that the length has got to be 4 anywhere within the hallway. And we know that if this angle's Theta, this angle over here must also be Theta. So if we want to find the hypotenuse but we know the adjacent, we want to find the hypotenuse, but we know the adjacent, We know that that's our secant formula. So we can see that a equal 4 secant Theta. When we look at this other triangle here, we know the opposite side and we want to find the hypotenuse. So the hypotenuse over the opposite is cosecant of the angle. So B is 7 cosecant Theta. So our length of our ladder is going to be 4 secant Theta +7 cosecant Theta. Now remember we could think of that as four over cosine Theta plus seven over sine Theta. So the next part wants us to grab our graphing calculators. So if we grab our calculator and let's go to the home key, let's look at settings to start, and we want to go to document settings. I recommend display digit always being on float, and we want to make sure we're in radiance. So hit make default. OK, then let's go to. I already typed it in, so I'm going to go to current document and we're going to do tab to bring back the line an arrow up once. So literally I typed in four divided by cosine XI have to use X because it's X here in the parenthesis plus 7 divided by sine X. Now the next thing we want to do is once we hit enter, we want to go to the menu key and we want to look at the window and it told us it wanted us to have zero to π / 2. So if I type in literally the Pi key divided by two and hit enter, oops, go back menu window, it actually types in what π / 2 is. And then it told us to do zero to 28. So I'm going to hit OK, so the next thing we're going to do is we're going to go to menu and we're going to do analyze graph and we want a minimum. So we're going to go to the left side, it's going to kind of shade in, we're going to go to the right side of where the minimum is, and we're going to see that this is our minimum location. So depending on how many points we have, if we click on this and then we tell it attributes, we can actually give ourselves more decimal places or less decimal places. So if we click on it, we do attributes and we can make it more or less decimal places as we need. So the angle it tells us to round to the nearest hundredth tenths hundredths. So .878 is going to round to .88. And then the length of the ladder is actually our Y value because remember this equation a minute ago was really just our length of the whole ladder. So the Y value and it wants it to the hundredths again. So 15.36 in this particular example. So if we went back into here we could see 0.88 is going to be our angle and 15.36 would be the length.