Question

Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AD = 1 and BD = 3, what is the length of AC ​

Answer 1

The length of AC is approximately equal to 3.162.

Explanation:

The length of AC can be calculated using the Pythagorean Theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the hypotenuse. So, for triangle ABC with AD = 1 and BD = 3, we have:

AC^2 = AD^2 + BD^2

AC^2 = 1^2 + 3^2

AC^2 = 1 + 9

AC^2 = 10

Taking the square root of both sides:

AC = sqrt(10)

So, the length of AC is approximately equal to 3.162.