Question

a 20 foot ladder rests against a building 15 feet from the floor. how far does the ladder extend from the base of the wall? what angle does the ladder make with the ground?

Answer 1

I believe this is the scenario , yes?

Answer 2

yes that's what i drew . i'm not sure how to get the angle from there

Answer 3

you could take the arc sine of 3/4

Answer 4

where did you get 3/4 from ?

Answer 5

first off that is wrong, so nvm
secondly, unless i am miss my guess the picture is wrong too!

Answer 6

how ? the 20ft is the ladder and the 15ft is the wall .

Answer 7

oh maybe not
fifteen feet from the floor might mean the height of the ladder

Answer 8

ok fine lets say that is right
then
\[\sin(a)=\frac{15}{20}=\frac{3}{4}\] so
\[a=\arcsin
(\frac{3}{4})\]

Answer 9

wow okay that makes sense . if the picture was wrong what would you do ?

Answer 10

now i think it is right
but if it is wrong and the 15 is along the ground, take the arc cosine

Answer 11

we say that:
\[\sin a=15/20 \\
\sin a =3/4 \\a=\sin^{-1}(3/4) \\
a\approx 48.6 degrees\]

Answer 12

\[x=20 \cos \left(\sin ^{-1}\left(\frac{15}{20}\right)\right)=5 \sqrt{7}=13.2288 \]

Answer 13

which is right ?? you all have different answers ...

Answer 14

The length of the unknown triangle side is:\[\sqrt{20^2-15^2}=5 \sqrt{7}=13.2288 \]The angle is:\[\frac{180 \sin ^{-1}\left(\frac{15}{20}\right)}{\pi }=48.5904 \text{ degrees} \]

Answer 15

what is the length of the third side ?

Answer 16

i doubt its a decimal but i could be wrong

Answer 17

never mind its right