Final answer:
To find the length of AC, we can use the Pythagorean theorem. Given BC = 10 and tan A = 5/12, we can find AB. Then, using the Pythagorean theorem, we can find AC.
Step-by-step explanation:
To find the length of AC, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.
Given that BC (leg) = 10 and tan A = 5/12, we can use the formula tan A = opposite/adjacent. In this case, the opposite side is the length of AB (leg) and the adjacent side is the length of BC (leg). So, tan A = AB/10, which gives us AB = 512*10 = 60.
Now, we can use Pythagorean theorem to find the length of AC: AC² = AB² + BC². Substituting the values we have, AC² = 60² + 10² = 3600 + 100 = 3700. Taking the square root of both sides, we get AC = √3700, which is approximately 60.83.