Angle of Elevation
Date: 01/22/97 at 21:11:59 From: David Subject: I need some help in the Geometry Area I working on angle of elevation and angle of depression right now and I have a question about this problem: A tree 66 meters high casts a 44 meter shadow. Find the measure of the angle of elevation of the sun. We are using cosine, sine, and tangent right now, so how do I do this problem using this information? Sincerely, David
Date: 01/22/97 at 21:51:44 From: Doctor Wallace Subject: Re: I need some help in the Geometry Area Hi David! Okay, the first thing to do in a problem of this sort is draw a picture. I hope you did that. I drew a line on the right side of my paper representing the tree. I labeled it 66m. The sun is higher than the tree, and to the right of it. I drew a straight line coming from the sun diagonally down to the left, touching the top of the tree and continuing on for some distance. This is the sunbeam. Now for the shadow. I drew a line perpendicular to the tree, from the bottom of the three to the left until it intersected the sunbeam. This line I labeled 44m. You notice that what you have drawn is a right triangle. The right angle is in the lower right, and you have 2 acute angles, one at the top right, and one at the bottom left. Okay so far? Now, the problem asks you for the angle of elevation of the sun. Do you know which of the triangle's angles this is? Pretend you are standing on the ground to the left of the tree, at the end of the shadow. You look up at the sun. The angle of elevation of the sun is how high the sun is above the ground from that point. So the lower left angle of the right triangle is the angle you're going for. Now, how to find it? Well, you mentioned that you need sin, cos, and tan. Good job. But which one? Well, sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent. You should be able to take it from here. Only one of these three trigonometric functions can be applied here (if you look at your triangle, you'll see that you don't know the length of the hypotenuse). Then you will have an equation like: angle of elevation = something divided by something Then you can either use a calculator or the table of trig functions in your math book to find the angle. -Doctor Wallace, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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