Answer:
x = 71°
Yes.
Explanation:
To solve for x, use the cosine trigonometric ratio. You can remember all of the trig. ratios with SohCahToa.
"Cah" tells us "cosine is adjacent over hypotenuse", or:
cosθ = adjacent / hypotenuse
θ means the angle of reference, or the angle we are talking about.
The hypotenuse is the longest side, usually looking slanted.
The adjacent side is touching angle θ and is not the hypotenuse.
Use the formula and substitute the sides.
cosθ = adjacent / hypotenuse
cosx = 4ft / 12ft Dividing two same units will cancel them out
x = cos⁻¹(4/12) Rearranged to isolate "x". Input into calculator.
x = 70.52877.....° Exact answer
x ≈ 71° Rounded answer
If 70° < x < 75°, the ladder is safe.
70° < 71°
71° < 75°
Since 71° is between 70° and 75°, the ladder is safe.