Question

In Exercises 75 and 76 , use the following information. The relationship between the length of an adult's femur (thigh bone) and the height of the adult can be approximated by the linear equations \(y=0.432 x-10.44\) \(y=0.449 x-12.15\) where \(y\) is the length of the femur in inches and \(x\) is the height of the adult in inches (see figure). An anthropologist discovers a femur belonging to an adult human female. The bone is 15 inches long. Estimate the height of the female.

Short answer

The estimated height of the female is approximately 59 inches.

Step-by-step solution

Identify the right equation

Since the femur is from a female, the equation to be used is \(y=0.432 x-10.44\), where \(y\) is the length of the femur and \(x\) is the height.

Substitute the given value

Substitute \(y\) with the given length of the femur which is 15 inches. The equation becomes: \(15 = 0.432x - 10.44\). This is a simple linear equation and it can be solved for \(x\).

Solve for \(x\)

To find \(x\) (height of the individual), we add \(10.44\) to both sides and then divide by \(0.432\). The equation becomes: \(x = (15 + 10.44) / 0.432).

Calculate

Upon calculation, \(x\) equals approximately \(59\).

Key concepts

Anthropometry

Anthropometry is a fascinating field of study that focuses on measuring and analyzing human body dimensions. This practice is crucial in various applications, such as designing ergonomic tools, creating spaces that fit human use, or in the case of forensic science, understanding past human populations through skeletal remains. Anthropometry enhances our understanding of human physical variation across different populations and time periods.

• Tools: Measurements in anthropometry can be as simple as using a tape measure or as sophisticated as employing 3D body scanners.
• Applications: It supports a broad range of fields, including health, nutrition, anthropology, and biomechanics.
• Data Utilization: Anthropometric data can help in designing better products, like more comfortable clothing or safer vehicles.

The science continues to evolve, incorporating advances in technology to improve accuracy and application scope.

Femur Length

The femur, or thigh bone, is the longest and strongest bone in the human body. As such, it plays a pivotal role in the study of human measurement for several reasons.

• Stability & Mobility: The femur supports a significant amount of the body's weight, providing both stability and mobility.
• Indicator of Height: Femur length is often used in anthropometric studies because of its correlation with an individual's height.
• Longitudinal Research: Studies focusing on femur length can reveal insights into the growth patterns and health conditions of populations.

In the context of height estimation, the measurement of a femur can offer valuable data, especially when studying remains where direct measurement is not possible.

Height Estimation

Height estimation is a useful skill in anthropology, especially when working with skeletal remains. It's a process where linear equations derived from statistical data are used to infer height. Typically, the length of long bones such as the femur provides a reliable means for this kind of estimation.

• Linear Equations: Equations are formed based on research data linking bone lengths to overall height.
• Application Example: For a discovered female femur measuring 15 inches, the calculation uses the specific equation for females: \(y = 0.432x - 10.44\). By inserting the bone length, we solve for \(x\), giving an estimated height.
• Importance: This method is especially useful in archaeological and forensic analysis, helping scientists understand ancient populations or solve modern cases.

The beauty of height estimation lies in its ability to reveal historical and biological information from mere bone fragments, anchoring a bridge between past and present human life.