Final answer:
To find the length of BD, we can use the Pythagorean theorem. We can obtain AC by using the cosine of angle A. Finally, we can solve for the length of BD using the Pythagorean theorem again.
Step-by-step explanation:
To find the length of BD, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's consider triangle ABC. We are given that AB = 12 and cos(A) = 15. Since cos(A) = adjacent/hypotenuse, we can solve for AC using the equation 15 = AC/12. Solving for AC, we find that AC = 12 * 15 = 180.
Now, we can use the Pythagorean theorem on triangle DBC. We know that CD = 2 and AC = 180. Let's denote BD as x. Applying the Pythagorean theorem, we get x^2 = 2^2 + 180^2. Solving for x, we find that x = sqrt(2^2 + 180^2).