Geometry Triangles

KevinVM20 · #1 $Old$ 08-31-2008, 11:35 AM

I was working on a problem. I know that I am supposed to solve for the unknown. I just don't know what exactly the unknown is.

Here is the problem-

I can look out my window and see the top of a tower. On the map, I see that it is 2 miles away. I read somewhere that the tower is 500 feet tall. As I look at the tower, I see that the top leaves of a tree sometimes get in the way of the top of the tower. The tree is 50 yards from where I sit. How tall is the tree?

How do I put this problem into an equation and what is the equation?

Thanks for all potential help.

Moo · #2 $Old$ 08-31-2008, 12:42 PM

Hello,

Quote:

Originally Posted by KevinVM20 $View Post$

I was working on a problem. I know that I am supposed to solve for the unknown. I just don't know what exactly the unknown is.

Here is the problem-

I can look out my window and see the top of a tower. On the map, I see that it is 2 miles away. I read somewhere that the tower is 500 feet tall. As I look at the tower, I see that the top leaves of a tree sometimes get in the way of the top of the tower. The tree is 50 yards from where I sit. How tall is the tree?

How do I put this problem into an equation and what is the equation?

Thanks for all potential help.

Do you know how to use the Intercept theorem ?

KevinVM20 · #3 $Old$ 08-31-2008, 01:08 PM

Soroban · #4 $Old$ 08-31-2008, 01:37 PM

Hello, KevinVM20!

To answer your first question:
. . the unknown is obviously the height of the tree.

Quote:

I can look out my window and see the top of a tower.
On the map, I see that it is 2 miles away.
I read somewhere that the tower is 500 feet tall.
As I look at the tower, I see that the top leaves of a tree
sometimes get in the way of the top of the tower. **
The tree is 50 yards from where I sit.
How tall is the tree?

** I assume this means that the top of tree lines up
. . with the line-of-sight to the top of the tower.

We further assume that your eye and the base of the tower are at the same height.

Let $h$ = height of the tree (in feet).
Change all units to feet.

Code:

                              *
                          *   |
                      *       |
                  *           | 500
              *   |h          |
          *       |           |
      * - - - - - * - - - - - *
      : -  150  - :
      : - - - 10,560  - - - - :

From the two similar right triangles, we have: . $\frac{h}{150} \:=\:\frac{500}{10,560}$

Therefore: . $h \;=\;\frac{75,000}{10,560} \;=\;\frac{625}{88} \;\approx\;7.1\text{ feet}$

KevinVM20 · #5 $Old$ 08-31-2008, 02:20 PM

Thank you very much Soroban! I now have a better understanding.

Quote:

Originally Posted by Soroban $View Post$

Hello, KevinVM20!

To answer your first question:
. . the unknown is obviously the height of the tree.

** I assume this means that the top of tree lines up
. . with the line-of-sight to the top of the tower.

We further assume that your eye and the base of the tower are at the same height.

Let $h$ = height of the tree (in feet).
Change all units to feet.

Code:

                              *
                          *   |
                      *       |
                  *           | 500
              *   |h          |
          *       |           |
      * - - - - - * - - - - - *
      : -  150  - :
      : - - - 10,560  - - - - :

From the two similar right triangles, we have: . $\frac{h}{150} \:=\:\frac{500}{10,560}$

Therefore: . $h \;=\;\frac{75,000}{10,560} \;=\;\frac{625}{88} \;\approx\;7.1\text{ feet}$