The answer is 78.5°.
The ladder and the building make up a right triangle. Knowing two sides, we can solve for the angle using SOH CAH TOA.
sinθ = O/H or opposite/hypotenuse
cosθ = A/H or adjacent/hypotenuse
tanθ = O/A or opposite/adjacent
*note: θ =angle
The hypotenuse is the longest side that is opposite the right angle. So in this case, the hypotenuse 10m. The opposite side is the side that is opposite the angle you are looking for, in this case the opposite is not given. The adjacent side is the side adjacent to the angle you are looking for, so in this case 2m.
Your given is then:
A = 2m
H = 10m
Now based on your given, you can decide which formula you are supposed to use to get the angle. Because CAH has both adjacent and hypotenuse, this is the formula you will use.
cosθ=A/H
[tex]cosx= \frac{A}{H} \\ cosx= \frac{2m}{10m} \\ cosx= \frac{1m}{5m} [/tex]
We transpose the cos to the other side and do the opposite of getting the cos, we use the inverse cosine.
[tex]x=cos^{-1}(0.2m) \\ x=78.5[/tex]
The answer is then 78.5°.
