Question

Archaeologists and forensic scientists use the length of human bones to estimate the height of individuals. A person's height, \(h\), in centimeters can be determined from the length of his/her femur, \(f\) (the bone from the knee to the hip socket), in centimeters using the following formulas: $$\text { Male: } h=69.089+2.238 f$$ $$\text { Female: } h=61.412+2.317 f$$ a. A partial skeleton of a male is found. The femur measures 50 centimeters. How tall was the man? b. What is the length of the femur for a female who is 150 centimeters tall?

Short answer

What is the femur length of a woman who is 150 cm tall? Answer 1: The man is approximately 180.989 centimeters tall. Answer 2: The femur length of the woman is approximately 38.239 centimeters.

Step-by-step solution

Understand the information provided

The exercise provides two formulas to determine a person's height, h, based on the length of their femur, f. The first formula is for males, and the second is for females. We'll need to use these formulas to solve the questions given.

Determine the height of the male with a 50 cm femur

For part (a), we are given the femur length (50 cm) of a male skeleton and need to determine his height. We will use the male formula to calculate the height: $$h = 69.089 + 2.238f$$ Now, we'll substitute the femur length (50 cm) into the formula: $$h = 69.089 + 2.238(50)$$ Calculate the height: $$h \approx 69.089 + 111.90 = 180.989$$ The man was approximately 180.989 centimeters tall.

Determine the femur length of a 150 cm tall female

For part (b), we are given the height of a female (150 cm) and need to determine the length of her femur. We will use the female formula and solve for the femur length: $$h = 61.412 + 2.317f$$ Now, we'll substitute the given height (150 cm) into the formula: $$150 = 61.412 + 2.317f$$ Rearrange the equation to solve for femur length f: $$f = \frac{150 - 61.412}{2.317}$$ Calculate the femur length: $$f \approx \frac{88.588}{2.317} = 38.239$$ The length of the femur for a female who is 150 centimeters tall is approximately 38.239 centimeters.