In a right triangle, the sine of an acute angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Therefore, if sinx° = 4/5, we can label the opposite side of angle x as 4 and the hypotenuse as 5.
Using the Pythagorean theorem, we can find the length of the adjacent side of angle x:
a^2 + b^2 = c^2
where c is the hypotenuse, a is the adjacent side, and b is the opposite side.
Plugging in the values we know, we get:
a^2 + 4^2 = 5^2
a^2 + 16 = 25
a^2 = 9
a = 3
So the adjacent side of angle x is 3.
Now, we need to find cos(90° - x). Using the cosine formula, we know that:
cos(90° - x) = sinx°
Substituting sinx° = 4/5, we get:
cos(90° - x) = 4/5
Therefore, cos(90° - x) is equal to 4/5.
Hope this helped (: