To find the value of the secant of an acute angle in a right triangle when the cosine of that angle is given, we can use the relationship between cosine and secant.
The definition of cosine (cos) is:
- cos(θ) = Adjacent / Hypotenuse
And the secant (sec) is the reciprocal of cosine:
- sec(θ) = 1 / cos(θ)
Given that cos(θ) = rac{3}{5}, we can calculate sec(θ) using the formula:
sec(θ) = 1 / cos(θ) = 1 / rac{3}{5} = rac{5}{3}
Therefore, the value of the secant for the acute angle in the right triangle is:
sec(θ) = rac{5}{3}