To answer your question, we first have to understand few concepts in trigonometry.
Cosine of an angle in a right triangle is defined as the ratio of the adjacent side (the side touching the angle) to the hypotenuse (the longest side of a right triangle, opposite to the right angle).
So, we denote it as: cos(angle) = adjacent_side / hypotenuse
Given that the cosine of the angle is roughly (4/5), and that the hypotenuse is 5, we can find the measure of the adjacent side by rearranging our equation to solve for the adjacent side:
adjacent_side = cos(angle) * hypotenuse
Substituting the given values, we have:
adjacent_side = (4/5) * 5 = 4
Now, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. We can use this theorem to find the length of the side opposite to the given angle (opposite_side or "op").
Rearranging the Pythagorean theorem to solve for the opposite side gives us:
opposite_side = sqrt(hypotenuse^2 - adjacent_side^2)
Substituting the calculated and the given values, we find:
opposite_side = sqrt(5^2 - 4^2)
= sqrt(25 - 16)
= sqrt(9)
= 3
Consequently, the side opposite (or "op") to the given angle measures approximately 3 units.