In a right-angled triangle, the adjacent side to angle theta has length 4 and the opposite side has length 3. What is the exact value of sec(theta)?
Answer and explanation
Correct answer: C. 5/4
By the Pythagorean theorem, the hypotenuse is sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5. By definition, cos(theta) = adjacent / hypotenuse = 4/5. The secant is the reciprocal of cosine: sec(theta) = 1 / cos(theta) = 5/4.
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