Entry:5
In thie entry, we're gonna touch on  how to find the missing lengths of a similar triangle. If you remember from entry 2, Similar triangles have the same shape, but they are scaled differently, so they may  be different sizes.
This is where you may need to use some base knowledge of proportions.
You can use proportions to figure out the side length.

If a triangle has a height of 12, length of 2 and hypoteneuse of 24
and a similar triangle has a height of 24, length of 4, but the  length of the hypotenuse isn't given, you can set up a ratio.
12/24
6/12
3/6
1/2
so the triangle is  1 half of the size as the larger one.
you can do this with any triangle, as long as at least one side length on each shape is given, then you can set up a ratio,  and work from there, getting the ratio, simplifying it and coming up with the fraction; whatever it may be


                                            Lets do a practice quiz!

On a sunny day, Michelle and Nancy noticed that their shadows were different lengths. Nancy measured Michelle's shadow and found that it was 96 inches long. Michelle then measured Nancy's shadow and found that it was 102 inches long.

a.	Who do you think is taller, Nancy or Michelle? Why?
b.	If Michelle is 5 feet 4 inches tall, how tall is Nancy?
c.	If Nancy is 5 feet 4 inches tall, how tall is Michelle?

Nancy is taller. Since the right triangles defined by their heights and their shadows are similar, then the bases of the triangles have to be proportional to the heights of the triangles (i.e., their body heights).

b. 

Converting Michelle's height into inches (64 inches) and setting up a proportion, you would have:

64 / x = 96 / 102, or

x = 68 

Converting 68 inches back to feet, Nancy is 5 feet 8 inches tall.

c. 

Converting Nancy's height into inches (64 inches) and setting up a proportion, you would have:

64 / x = 102 / 96, or

x = 60.24

Converting 60.24 inches back to feet, Michelle is approximately 5 feet and 1/4 inch tall.