9514 1404 393
Answer:
3 in
Step-by-step explanation:
The distance of the midpoint to the line is half the difference of the distances of A and B to the line.
(10 in - 4 in)/2 = 3 in
O is 3 in from the line.
The distance between the midpoint O of the segment AB and line I is 3 inches.
The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The base is the adjacent smaller side of the angle θ.
As we can see in the two triangles, the tangent function of the trigonometry can be written as,
[tex]\dfrac{10}{x+y} = \dfrac{4}{x-y} \\\\10(x-y)=4(x+y)\\\\10x-10y =4x+4y\\\\10x-4x=10y+4y\\\\6x=7y\\\\\dfrac{x}{y}=\dfrac{7}{3}[/tex]
Thus, the value of x and y is 7 and 3 respectively.
Hence, the distance between the midpoint O of the segment AB and line I is 3 inches.
Learn more about Tangent (Tanθ):
https://brainly.com/question/10623976
