Question 701262
If you draw a diagram of the situation you should be able to see a right angled triangle formed by the wall and the floor and the ladder will be the hypotenuse.
The base of the triangle is 1 metre, and the hypotenuse is 3.5 m.
The angle at the base of the triangle that the ladder makes with the wallis found by using trigonometry.
Since we know the side adjacent (next to) the angle and the hypotenuse we have to use the cosine ratio.
{{{Cosine (angle) = (side_adjacent_to_the_angle)/hypotenuse}}}
Therefore
{{{Cosine(angle) = (1/3.5)}}}
therefore we find that
{{{Cosine(angle)=0.285714285714...)}}}
to find the angle that has this cosine we use the inverse function of the cosine which is known as the arccosine
so
{{{arccos 0.572814... = angle}}}
using a calculator we find that
angle = 73.398 degrees.