Question

A 25-foot ladder rests against a vertical wall. The foot of the ladder is 10 feet from the wall. What angle does the ladder make with the wall?
Which of the following expressions represents the angle the ladder makes with the wall?

cos-10.4
sin-10.4
tan-10.4

Answer 1

Here's your illustration:

I don't know if you can see that picture, but it's not showing up on my screen, so I'll describe it to you:
-Draw a right triangle
(It's a right triangle because the wall is vertical so the wall creates a right angle with the ground)
-The hypotenuse [the slanted side opposite the right angle] is your ladder. The length of the ladder is 25, so the length of your hypotenuse is 25.
-The long leg of the triangle [the long side that is not the hypotenuse] is your wall. We don't know the length of the wall, but that's okay for this problem.
-The short leg of the triangle [your shortest side] is the distance between the bottom of the ladder and the bottom of the wall. That's 10.

So you have your triangle. The angle the ladder makes with the wall is the angle between the top of the ladder and the top of the wall.
Your answer depends on the equation you're going to use to find this angle.
That depends on what lengths are given to you, which in this case is the hypotenuse and the short leg.
Your angle is opposite the short leg. This means the angle is not the right angle, and not an angle touching the short side.
The sine ratio is opposite side/hypotenuse
You have both the opposite side of the angle and the hypotenuse, so your formula would be this:
sin(angle)=10/25

So your answer would use the sine ratio, meaning your answer is...

sin-10.4

And there's your answer.