kcla1996 2 years ago 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

1. kcla1996

2. e.mccormick

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

rules of similar triangles?

4. e.mccormick

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

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

6. kcla1996

they are different

7. e.mccormick

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

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

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

10. kcla1996

120 ft?

11. e.mccormick

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

280 ft?

13. e.mccormick

120*2=? 280? Umm..

14. e.mccormick

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

15. kcla1996

240?

16. e.mccormick

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

no i dont know

18. e.mccormick

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

19. e.mccormick

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

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.