## kcla1996 Group Title Use the information in the diagram to determine the height of the tree to the nearest foot. A. 80 ft B. 264 ft C. 60 ft D. 72 ft one year ago one year ago

1. kcla1996 Group Title

2. e.mccormick Group Title

OK. The double hash marks mean the tree to building distance is the same as the tree to observer. Now use rules of similar triangles and that one bit of information.

3. kcla1996 Group Title

rules of similar triangles?

4. e.mccormick Group Title

Yes, if two triangles have the same shape, they are similar. Well, the tirangle from observer to building and observer to tree are similar. So the sides are rations of one another. Or, you can use trig to do the same thing. All depends on what you want to use, mathematically it is the same answer, but similar triangles is easiest in this case.

5. e.mccormick Group Title

Because that is true, what can you say about the ratio of the sides of the two triangles?

6. kcla1996 Group Title

they are different

7. e.mccormick Group Title

Well, the lengths of the sides are different, that is true. But there is a ratio between them. Let me see if I can find an easy reference on this principal that will make it clear.

8. e.mccormick Group Title

http://www.mathsisfun.com/geometry/triangles-similar.html That explains what similar triangles are. Now, because the observer to top of building to bottom of building triangle and the observer to top of tree to bottom of tree triangle are similar, you can use these rules here.

9. e.mccormick Group Title

Start by finding the total length from the observer to the building.

10. kcla1996 Group Title

120 ft?

11. e.mccormick Group Title

That is the distance from the observer to the tree. Now, look at the edited picture where I circled those marks. If obserevr to tree and tree to building are the same, what is observer to building?

12. kcla1996 Group Title

280 ft?

13. e.mccormick Group Title

120*2=? 280? Umm..

14. e.mccormick Group Title

You overshot there.... and I still make those mistakes in college, so it is not too surprising. Try again.

15. kcla1996 Group Title

240?

16. e.mccormick Group Title

Yes. Now, do you know how to set up the ratio of the sides? You have the unknown height of the tree, the height of the building, the distance from the observer to the tree and the distance from the observer to the building. They need to be in a ratio and solved for the unknown one.

17. kcla1996 Group Title

no i dont know

18. e.mccormick Group Title

OK. I am doing another editid pic. That will help explain it.

19. e.mccormick Group Title

Now, we now know that A=240. You are given the 120 and B=160. But C is the question. Tha is what we are dealing with. Now, do you know what a ratio is and how to solve them? If not, I can do a quick example.

20. e.mccormick Group Title

Basic ratios: If 10 is to 30 as 7 is to x, what is x? This can be set up as a ratio one of two ways. $\frac{ 10 }{ 30 } = \frac{ 7 }{ x } \,or\, \frac{ 30 }{ 10 } = \frac{ x }{ 7 }$Either way you then solve for x. If 10 and 30 are two sides of a triangle and 7 and x are two sides of a similar triangle, this type of ratio can be used to solve for the unknown side of the second triangle. That is why ratios can solve this problem.