Question

Phil is standing x+5 feet from the base of a building. The height of the building is 6x−1 feet. Find the function that the straight-line distance from Phil's feet to the top of the building in terms of x. Enter the simplified function.

Answer 1

`f(x)=\sqrt{37x^(2)-2x+26}`

Explanation:

we know that

To compute the required distance, using properties of triangles

Applying the Pythagoras Theorem

see the attached figure to better understand the problem

`PT^(2)=(6x-1)^(2)+(x+5)^(2)`

convert to expanded form

`PT^(2)=36x^(2)-12x+1+x^(2)+10x+25`

`PT^(2)=37x^(2)-2x+26`

square root both sides

`PT=\sqrt{37x^(2)-2x+26}`

Convert to function notation

`f(x)=\sqrt{37x^(2)-2x+26}`