The side opposite the greater angle is greater, so AC is greater than the length of the tree AB. The height (or rather length) of the tree, AB, is opposite a 40-degree angle. The distance to the house, AC, is opposite a 70-degree angle. Here is the picture, abstracted from the problem itself, labeled, and with the third angle labeled, ready to work on: Now, what is the angle at the top of the triangle, angle B? Since the sum of the angles in a triangle is 180 degrees, that angle is 70 degrees. I am assuming that the tree is tilted toward the house. You don't need trigonometry to answer your basic question, which is, could the tree hit the house? There is a theorem in geometry (it's Euclid's Proposition 19) that says: "In any triangle the side opposite the greater angle is greater." Let's see how we can use this. A simple inequalityĭoctor Rick answered, with a quick solution, and ignoring my little issue: Hi, Billy. In word problems, we generally don’t worry about real-life details like this, but if this is a real decision that has to be made, then we should. We’ll assume, as in the picture, that the angle to the top of tree was measured from the ground if it was measured at eye level, say 5 feet up, then the tree would be about 5 feet taller than our calculation: Presumably the tree is tilted toward the house, so it would fall in that direction: I haven't taken trig yet, so could you please help me out? Thanks. I read somewhere that if you have 2 angles and a side you can figure out the dimensions of the triangle. My family is worried that if we have a big storm the tree will fall and hit the house. The angle from our house to the top of the tree is 40 degrees. Our house is 66 1/2 feet away from the tree. There is a tree out in front of our yard. Let’s start with this real application from 1999: Will the Tree Hit the House?
We’ll be using the Law of Sines, and also exploring alternative methods of solution.
Having just looked at how to solve oblique triangles, let’s look at a couple “word problems” (applications) involving such triangles.