Equalateral Triangles and 30-60-90s

What is an equilateral triangle?






How can we find the height of these three equilateral triangles? 



What observations can we make about the equilateral triangles?
 Equilateral Triangle
* All sides Equal
* < sum is 180
* all <'s = 60
* if you cut in half 2 rt triangles
* neg space makes a square
* no hypot.
* no rt. < so no pythog.
* a 2 = b 2 = c 2
* just find one side length to find perimeter


What generalizations can we make?



HW:Due Tomorrow
On a 30, 60, 90 triangle (right triangle),  describe the relationship between the side length in generalizable terms and why is makes sense.

L-5 Same page as reflection

If you have a 30-60-90 and this side length is 36.What are the other side lengths?

 

18 and 18 square root of 3.

√

√

√

√

Sneaky Sally

Sneaky Sally

Can you make some observations about this picture?

 

*Area=8100 ft (90 x 90) 

*Square

*Homeplate + 1st base are adjacent <'s 

*Cut field in half get 2 right triangles

*Perimeter=360 (90+90+90+90)

*2 parallel sides, 2 sets of perpendicular sides  

Who is Sneaky Sally? 

-She steals bases and she is really good at it. 

-Good stealer usually steal 1st to 2nd. 

-It's a catchers job to throw the ball from home plate to 2nd base, if Sally steals that base. 

Question: How far does the catcher have to throw to get sneaky sally out? To second base.

Question: How far is the short stop from the catcher? 

info:Where does the short stop stand in this baseball diamond? 

-Ms.O'toole said he is standing halfway between 2nd and 3rd base. 

Question: How far is the pitcher's mound from each of the bases?

info:The Pitcher's mound is 60 ft and 6 inches away from home plate.

Question: How far does the catcher have to throw to get sneaky sally out? From the catcher to second base.

√16200 or 127 ft

Question: How far does the catcher have to throw to the short stop, if the short stop is halfway from 2nd to third base? 

Question: How far is it from the pitcher's mound to first base?2nd base? 3rd base? 

2nd base-  127-60.5=66.5ft from pitchers mound to 2nd base

Pythag Theroem

a²+ b²=c²

If I take the square root of the area, I get the side length.


What does it help us do? Why use it?
-It helps us to figure out side lengths
-It helps us to find the hypotenuse

Are there any real life situations?

Obtuse and Acute triangles?

L1

With a right triangle-

a²+ b²=c²

What do you think the relationship would be with an obtuse or acute triangle?  

We notice for obtuse the square is much bigger. 

We notice for the acute the square is much smaller or almost the same.  

Acute
a²+ b²>c²

Obtuse

a²+ b²<c²

What do I get when I square the square root of 13? 

13  

What is a cube root?

R-54 What do we know about square root?
2D
area
x²

A=l x w

√9=3

√=side length

What is a cube root? 

3D

A=l x w x h

Larger area/perimeter

Volume??

A= X x X x X

x=side length (outside of a 2D shape)

Inside of a cube is called volume. 

Cube with:

h=4

w=4

l=4

volume of 64. 

Show us on the cube where the 4 would go and the 64 would go? 

The class thinks that in a cube all the sides have to be the same. 

What are we going to call this? 

dimensions or x

What is the cube root of something equal to? 

³√= 

Should we call it volume, area, dimensions? 

Class determined: Dimensions

(outside of a 3D shape)

³√= 64 (volume)-inside

How are volume and area different? 

volume has a H x W x L

Can you draw a 3D shape with a volume of 27? What are the dimensions?
3³ or 3 x 3 x 3 
³√=27



³√125=5  What does the 125 mean in this math expression?
-The volume of the cube

What does the 5 mean?
-the dimensions of the cube

³√64=8
8=Side length of the square
64=area of a sqaure


Only a square has all the sides the same

HW: L57- pg. 32 # 50-5, 56-58, 60-64

Quiz Tomorrow!

What is a square root?

The side length

How can we find the area?