Question

A 28ft ladder is leaning against the side of a building. the base of the ladder is 8 ft from the base of the building. what is the measure of the angle formed by the base of the ladder and the ground

Answer 1

My go-to first step - draw a diagram!
Now it's easier to identify which sides are what and just generally solve the equation.

The ladder is 28 feet. The distance between the base of the ladder and the wall is 8 feet. And we are trying to find the angle where the base of the ladder meets the ground. Draw this up.

Now we identify which sides are what. I like to just subtly abreviate hypotenuse to H, Opposite to O, and Adjacent to A. Now look at the sides which we have the lengths of. 28 feet is the hypotenuse, and 8 feet is the adjacent!

Now we need to decide what to use - sine, cosine, or tangent. Looking at SOH CAH TOA, we can see that CAH has both the adjacent and the hypotenuse, which is just what we need.

When we are using SOH CAH TOA to find an angle, always remember to use the anti-cosine button instead of the cosine button on your calculator. It will read cos^-1 instead of cos if you did it right.

Now after typing in anti-cosine, we can substitute in the numbers, remembering that the adjacent is divided by the hypotenuse in this case.

Now calculate. The answer should be 73.4. If you get a strange looking answer like 1.28 or something, double check that your calculator is not in radians mode.

Hope I helped :D