4. A 25-foot ladder is placed against the side of a building with the bottom of the ladder 7 feet from the base of the building. If the base of the ladder is pulled back an additional 8 feet from the building,
how far will the ladder slide down the side of the building?

Step-by-step explanation:

The questions asks for how far down the wall does the ladder move, so to say that in another way,   what is the difference between when the ladder is taller up the wall and when it is shorter up the wall.

so figure out what the height of the ladder is up the wall for each of the situations.

1) Taller

we are told the Hyp and the Adj sides of the triangle

so  use  SOH CAH TOA to remind how trig functions fit on the triangle  sin = Opp / Hyp , Cos=Adj / Hyp ,  Tan = Opp / Adj  so

Cos(Ф) = 7 / 25

Ф = arcCos( 7/25)

Ф = 73.739795 °

then use

Sin( 73.739795 ) = Opp / 25

25* Sin( 73.739795 ) = Opp

24 = Opp

2) Shorter

Cos(Ф) = 15 / 25

Ф = arcCos( 15 / 25 )

Ф = 53.13010 °

sin( 53.13010 ) = Opp / 25

25 * sin( 53.13010 ) = Opp

20 = Opp

now you know the two heights up the wall. so subtract the shorter from the taller

24 - 20 = 4

the ladder moves 4 feel down the wall  :)

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step-by-step explanation: