How to Determine Height by a Cast Shadow

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So long as an object is casting a shadow, you can determine its height in just a few easy steps. Determine height by a cast shadow with help from an experienced educator in this free video clip.

Part of the Video Series: Lessons in Math
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Video Transcript

Hi, my name is Marija. I'm a mathematician, and today I'm going to show you how to determine height by a cast shadow. So, normally, these problems start with a tree or a person, so we're just going to draw a person, and you're going to have his shadow cast on the ground. And however far they tell you his shadow is on the ground, let's say his shadow is ten feet from his feet. We're not going to draw it as an actual shadow. You're going to draw a straight line, so we can eventually construct a right triangle. So, we're going to do ten, right here. Now, what you're looking for is this man's height. So, you want to go ahead and draw a vertical line upwards. That's a 90 degree angle representing his height, which is what we're looking for. And you want to be able to construct a right triangle. Now, the other piece of information that you have to be given is the angle of elevation from the ground to the man's head. So, I'm going to draw that. I'm going to say that the angle of elevation that was given to me is 25 degrees. Now, you could also have been given the hypotenuse, and then you would have had to work around it a little bit differently. So, we'll do it in a situation where you're giving an angle, and you're given a side. Now we're using trigonometry, and you have to figure out which ratio you're going to use. So, always remember SOHCAHTOA, and know that you have to see which relationship you have. Well, from the angle I have the opposite and I have the adjacent. So, I see that I'm using T. I'm using tangent. So, I'm going to set up my equation as tangent of 25 equals opposite. So, it's going to be H over adjacent, which is ten. Now, like in any other equation, I'm solving for the variable. It's being divided by ten. So, I'm going to multiply both sides by ten. And that means that the height of this man is ten tangent 25. And you can go ahead and just put that right in your calculator. Ten multiplied by the tangent of 25, and that'll give you the height of the man. My name is Marija, and I just showed you how to calculate for height when you are given a shadow that is cast.

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