Final answer:
To sketch a right triangle with sec(θ) = 13/5, we can use the Pythagorean identity and the Pythagorean theorem. The possible side lengths for the triangle are 5, 12, and 13.
Step-by-step explanation:
To sketch a right triangle, we first need to determine the side lengths. The given information is that the value of sec(θ) is 13/5. Secant is the reciprocal of cosine, so we can use the Pythagorean identity to find the side lengths. Since sec(θ) = hypotenuse/adjacent, we have cos(θ) = 5/13. From this, we can use the Pythagorean theorem to find the other side lengths. Let's assume the adjacent side is 5. Then, the opposite side will be 12 and the hypotenuse will be 13. So the possible side lengths for the right triangle are 5, 12, and 13.