Final answer:
The length of AB in the given right triangle can be found using the Pythagorean theorem and the similarity of triangles.
Step-by-step explanation:
Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AD=6 and AC=15, the length of AB can be found using the Pythagorean theorem.
Since BD is the altitude, it divides the triangle into two smaller triangles, ABD and CBD.
Both of these triangles are similar to the original triangle ABC.
Using the similarity of the triangles, we can set up the following proportion: AB/AD = AC/AB.
Substituting the given values, we have AB/6 = 15/AB.
Cross-multiplying gives AB^2 = 6 * 15, which simplifies to AB^2 = 90.
Taking the square root of both sides gives AB = √90, which simplifies to AB = 3√10.