I know that to find the height of a woman that has a tibia bone measuring 43.4 would be computed like this

H(t)=0.984(t)+28.6, and I would arrive at this :69.5696, but I how would I prepare a function to figure out a womeans tibia in inches when she is 5 foot, 5 inches. I am stuck.

I believe the formula should be something like:

H(t)=2.45t+28.6,
where t=tibia length measured in inches
28.6=constant in inches.
The formula varies with the race of the individual (the given one is for negroid female, in inches), and the original formula was for measurements in centimeters (1"=2.54 cm). The 28.6 came from a conversion from (72.56) cm to inches, but the factor 2.45 was probably inadvertently divided by 2.54 also.
See:
http://www.pbs.org/saf/1203/teaching/teaching2.htm

Now to answer the question, if
H(t)=mt+b, where m and b are constants, and t the independent variable representing the length of the tibia bone, we look for the inverse of the function H(t) such that
H-1(h)=T(h)=ph+q where
p and q are constants derived from m and b, and T(h) is the tibia bone length, and h=body height.

To find the inverse of a function, we follow the following steps:
Let
h=H(t)=mt+b
solve t in terms of m, b, and h:
t=(h-b)/m
=(1/m)h - b/m
Therefore
T(h)=(1/m)h - b/m

For the given constants,
m=2.45, b=28.6, we get
T(h)=0.408h-11.67

For example, if the tibia bones measures 15", then
body height, h
= H(15)
= 2.45*15 + 28.6"
=65.4"

The inverse function is T(h), for a height of h=65.4,
T(65.4)=0.408*65.4-11.67
=15.0".

To figure out a woman's tibia length in inches when she is 5 feet 5 inches tall, you can follow these steps:

Step 1: Convert the height from feet and inches to inches.
To convert 5 feet 5 inches to inches, you can multiply 5 by 12 (since there are 12 inches in a foot) and then add the remaining 5 inches. This gives you:
Total inches = (5 * 12) + 5 = 60 + 5 = 65 inches.

Step 2: Use the given function to calculate the tibia length.
The given function is H(t) = 0.984(t) + 28.6, where H(t) represents the height in centimeters and t represents the tibia length in centimeters.

To convert the height from inches to centimeters, you can use the conversion factor: 1 inch = 2.54 centimeters.

So, the updated function for tibia length in inches would be:
TibiaLength(in) = 0.984 * (TibiaLength(cm)) / 2.54

Step 3: Plug in the height in inches into the function.
Substitute the height of 65 inches into the updated function:
TibiaLength(in) = 0.984 * (65) / 2.54

Step 4: Calculate the tibia length in inches.
Using a calculator, evaluate the expression:
TibiaLength(in) = (0.984 * 65) / 2.54 ≈ 25.22992 inches.

Therefore, if a woman is 5 feet 5 inches tall, her tibia length would be approximately 25.23 inches.