To find the value of the secant (sec) of an acute angle in a right triangle where the cosine (cos) is given as 3/5, we start by recalling the relationship between cosine and secant.
The secant of an angle, denoted as sec(θ), is the reciprocal of the cosine of that angle. In mathematical terms, this can be expressed as:
sec(θ) = 1 / cos(θ)
Given that cos(θ) = 3/5, we can substitute this value into our equation:
sec(θ) = 1 / (3/5)
To divide by a fraction, we multiply by its reciprocal:
sec(θ) = 1 * (5/3) = 5/3
Therefore, the value of sec(θ) is 5/3. This means that the secant of the acute angle in this right triangle is 5/3.