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Answer :
The angle of elevation of the femur is 71°.
The angle of elevation:
The angle is formed by the line of sight and the horizontal plane for an object above the horizontal.
Here we have to find the angle of elevation of the femur.
Data given:
length of femur = 18 inches
elevated = 6.2 inches
Formula to calculate the angle of elevation:
Tangent of the angle of elevation = height of the object/distance from the object
tan Ф = 18/ 6.2
tan Ф = 2.903
Ф = [tex]tan^{-1}[/tex]( 2.903)
= 71°
Therefore the angle of elevation is 71°.
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Final answer:
The angle of elevation of the femur can be found using the inverse tangent function, based on the elevation of 6.2 inches and the length of 18 inches, using the formula [tex]\(\theta\) = tan-1(6.2/18)[/tex].
Explanation:
To calculate the angle of elevation of the femur, we use trigonometric functions, particularly the tangent function because we have the opposite side (elevation of the femur) and the adjacent side (length of the femur) of the right triangle formed. The formula for the tangent of an angle in a right triangle is [tex]tan(\(\theta\)) = opposite/adjacent[/tex], where [tex]\(\theta\)[/tex] is the angle of elevation.
Here, the opposite side (elevation) is 6.2 inches and the adjacent side (length of the femur) is 18 inches. So we have [tex]tan(\(\theta\)) = 6.2/18[/tex]. Using an inverse tangent function (arctan or tan-1), we can find the angle \(\theta\).
[tex]\(\theta\) = tan-1(6.2/18)[/tex]
