Question

Can someone answer this question quickly for me?
A 12 Foot ladder leans against a wall, making an angle of 40 Degrees with the horizon. How far is the base of the ladder from the wall?

Answer 1

cos(40) = x/12

solve for x

Answer 2

Now if we look at the drawing we see that we know of the hypotenuse but want to know of the side that is closest to the angle which is defined as the adjacent side so there is only one trig ratio which deals with the hypotenuse and the adjacent side which is cosine....so we would write down the ratio of cosine...

\(\Huge{\cos(x)=\frac{adjacent}{hypotenuse}}\)

Now we know the angle is 40 in which we input where x is, and we also know that the hypotenuse side is \(\Large{12}\) and that we want to know of the adjacent side so we input this....

\(\Huge\color{purple}{\cos(40)=\frac{x}{12}}\)

Now since the known number is in the denominator we would multiply \(\Large{12}\) by cosine so....

\(\Huge\color{red}{12 \times \cos(40)=x}\)

Note: When inputting this into the calculator make sure to have it set in degree mode not in radian mode.

Answer 3

Were you able to understand this @Cam7661 ?