 These problems of angles of elevation and depression are the exciting When am I the world am I ever going to use this kind of problems? This takes the trigonometry that you've learned about and applies it to actual real-world problems Real-world problems that we've really had to solve the angle of depression the second video is a real-life problem My husband asked me about and I was able to solve it with trigonometry. I Want you to get out your worksheet the angles and elevation and depression worksheet and on the back side I want you to find number five so find number five on your worksheet pause the video get out the worksheet and find number five So a guy wire is attached 30 feet from the top of the hundred foot tower So I've got a hundred foot tower here and the guy wire is attached 30 feet down from the top One of the reasons I'm doing this problem is students always ask what a guy wire is guy wire helps brace A tall skinny thing like a radio tower or something so that it doesn't blow over in the wind. It's a it helps Make the tower more sturdy because of the properties of trigonometry To continue on the guy wire makes it 55 degree angle with the ground And the question is what's the length of the wire? So I'll call the guy wire X or the length of the guy wire X From the angle here the things I know the the distance I know is the opposite I can figure out how high up that guy wire is attached to the Radio tower or tower and the thing I want to know is the hypotenuse here So if I'm trying if I'm working with an angle with the opposite and the hypotenuse The function is going to be sine So the sine of 55 is going to be the opposite the opposite Length of the the distance up that that triangle makes the opposite length is 70 feet Because the full tower is a hundred feet the wire is attached 30 feet down that makes the distance from the ground To where the wire is attached 70 feet So the sine of 55 equals the opposite which is 70 Over the hypotenuse Which is X Now it's been suggested to turn this into a proportion makes it much easier to solve If you think of it as a proportion so I can say the sine of 55 over 1 equals the opposite over the hypotenuse so pause the video now and Do your cross multiplying? Multiply as I would say in an X Pause the video and work out that multiplication problem Okay, when I multiplied I got that X times the sine of 55 Equals 70 times 1 so it's 70 now. I want to solve for X. So I'm going to do what on both sides I'm going to divide both sides by the sine of 55 Sorry my five got a little goofy there running out of room simplifying I get That X equals 70 divided by the sine of 55 At this point I pick up my calculator and do the calculations pause the video right now You get your calculator and run the numbers see what you get On my calculator. I get that X equals 85 point four five four two Seven etc. So I'm going to say to the tenths place. My final answer is that the length of the guy wire is 85 point five and the unit is feet So here's one example of how trigonometry actually helps us figure out Real-life problems that we want to solve Enjoy this move on to the angle of depression video and have fun with these With these actual problems