Question

Given right triangle ABC with altitude ‾BD drawn to hypotenuse ‾AC, if ‾AC =55 and ‾DC=15, what is the length of ‾BC in simplest radical form?

Answer 1

To find the length of ‾BC, we use the Pythagorean theorem and substitute the given values to solve for the unknown length. The length of ‾BC is found by subtracting the length of ‾BD from the length of ‾AC.

Step-by-step explanation:

To find the length of ‾BC, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs. In this case, ‾AC is the hypotenuse and ‾BD and ‾DC are the legs. We are given that ‾AC = 55 and ‾DC = 15.

Using the Pythagorean theorem, we can write the equation: ‾AC^2 = ‾BD^2 + ‾DC^2.

Substituting the given values, we get 55^2 = ‾BD^2 + 15^2. Solving for ‾BD, we find that the length of ‾BD is 50.

Finally, to find the length of ‾BC, we subtract ‾BD from ‾AC: ‾BC = ‾AC - ‾BD = 55 - 50 = 5.