Archaeologists and forensic scientists use the length of of human bones to estimate the height of his/her femur f(the bone from the knee to the hip socket), in centimeters using the following formulas:
Male h=69.089+2.238f Female: h = 61.412+2.317f
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?
a. 69.089 + 2.238(50)
b. 150 = 61.412+2.317f
150-61.412 = 2.317 f
(150-61.412)/2.317 = f
A) 180.989
a. To find the height of the man, we use the formula for males:
h = 69.089 + 2.238f
Given that the femur measures 50 centimeters, we can substitute f = 50 into the formula:
h = 69.089 + 2.238(50)
h = 69.089 + 111.9
h = 180.989 centimeters
Therefore, the man's estimated height is approximately 180.989 centimeters.
b. To find the length of the femur for a female who is 150 centimeters tall, we use the formula for females:
h = 61.412 + 2.317f
Given that the female's height is 150 centimeters, we can substitute h = 150 into the formula:
150 = 61.412 + 2.317f
Subtracting 61.412 from both sides:
88.588 = 2.317f
Dividing both sides by 2.317:
f ≈ 38.2 centimeters
Therefore, the length of the femur for a female who is 150 centimeters tall is approximately 38.2 centimeters.
To calculate the height of a person based on the length of their femur, you can use the corresponding formula based on the person's gender.
a. To determine the height of a male based on a 50-centimeter femur length, use the formula:
Male: h = 69.089 + 2.238f
Plug in the given femur length, which is 50 centimeters, into the formula and solve for 'h':
h = 69.089 + 2.238(50)
h = 69.089 + 111.9
h = 180.989
Therefore, the man's height is approximately 180.989 centimeters.
b. To find the femur length for a female who is 150 centimeters tall, use the formula:
Female: h = 61.412 + 2.317f
Plug in the given height, which is 150 centimeters, into the formula and solve for 'f':
150 = 61.412 + 2.317f
150 - 61.412 = 2.317f
88.588 = 2.317f
f ≈ 38.215
Therefore, the femur length of a female who is 150 centimeters tall is approximately 38.215 centimeters.