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

Answer:

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

Step-by-step 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

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