Question

A ladder 23 feet long leans against the side of a building, and the angle between the ladder and the building is 25°.
(a) Approximate the distance from the bottom of the ladder to the building. (Round your answer to two decimal places.)
__ft

(b) If the distance from the bottom of the ladder to the building is increased by 2.0 feet, approximately how far does the top of the ladder move down the building? (Round your answer to two decimal places.)
__ft

Answer 1

Yep got that part

Answer 2

oh we should also label the distance from the base of the ladder to the wall
lets call it \(x\)

Answer 3

then
\[\cos(25)=\frac{x}{23}\] an so
\[x=23\cos(25)\] and a calculator

Answer 4

22.797

Answer 5

since for right triangles, cosine is "adjacent over hypotenuse"

Answer 6

yeah so it would be 22.80 ??

Answer 7

feet

Answer 8

that is not what i get

Answer 9

what did you get?

Answer 10

http://www.wolframalpha.com/input/?i=23cos%2825%29

Answer 11

not sure why our answers should be different
when i am on a computer i always use wolfram

Answer 12

Weird, neither of those are right. My homework offers unlimited trys

Answer 13

how many decimal places does it want?

Answer 14

two

Answer 15

ooooh damn! i should learn to read
lets try again

Answer 16

says the angle with the BUILDING not the ground

Answer 17

in this case
\[\sin(25)=\frac{x}{23}\] making your answer
\[x=23\sin(25)\]

Answer 18

YEAH! i had it drawn that exact same way and i just figured i was wrong and you were right haha cause you looked smart. Pshh i should trust myself.

Answer 19

http://www.wolframalpha.com/input/?i=23sin%2825%29
try \(9.72\)

Answer 20

oh yeah i am not very smart, especially at reading

Answer 21

yep that's correct

Answer 22

so then for B) it would be 11.72

Answer 23

i don't know
lets see if we can do this without me screwing up
the distance we know was \(9.72\) and now it is \(11.72\) but it is not asking for you to add 2 to the distance of the bottom of the ladder from the building, but now it is asking for the decrease in the height of the ladder

Answer 24

you can now find the distance from the bottom of the building to the top of the ladder by pythagoras, since you have two sides of a right triangle, the hypotenuse \(23\) and the base of the triangle \(11.72\)

Answer 25

so you need two numbers, the original height of the ladder, which was
\[\sqrt{23^2-9.72^2}\] and the new height
\[\sqrt{23^2-11.72^2}\]

Answer 26

subtract the second from the first to see how far down it moved

Answer 27

wonder if i messed that one up too?

Answer 28

no that looks right

Answer 29

I got 19.7899

Answer 30

soo 19.79

Answer 31

http://www.wolframalpha.com/input/?i=sqrt%2823^2-9.72^2%29-sqrt {23^2-11.72^2%29

Answer 32

can't have moved down as far as you said
now sure my answer is right, but positive it is not 19.79

Answer 33

oh you have to copy and paste the link i sent
it wont open as it is

Answer 34

wont let me copy it

Answer 35

what did you get?

Answer 36

try this
http://www.wolframalpha.com/input/?i=sqrt%2823^2-9.72^2%29-sqrt%2823^2-11.72^2%29

Answer 37

seems more reasonable
bottom increases by 2, top decreases by \(1.06\)

Answer 38

Okay that was right! i get it now, wow i was way off

Answer 39

oh it was right? guess i redeemed myself for the first dumb error

Answer 40

Yep, thank you very much! i owe you big time

Answer 41

Would you be able to help me with another problem? if you have time?

Answer 42

@satellite73