Question

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

Answer 1

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.

Answer 2

rules of similar triangles?

Answer 3

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.

Answer 4

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

Answer 5

they are different

Answer 6

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.

Answer 7

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.

Answer 8

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

Answer 9

120 ft?

Answer 10

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?

Answer 11

280 ft?

Answer 12

120*2=? 280? Umm..

Answer 13

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

Answer 14

240?

Answer 15

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.

Answer 16

no i dont know

Answer 17

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

Answer 18

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.

Answer 19

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.