On right triangle upper A upper C upper B, the altitude of vertex upper C is drawn as a solid line that extends from upper C to the hypotenuse, upper A upper B. The intersection of the altitude and upper A upper B is labeled upper D.

Question

Given is the right triangle ABC
with altitude CD
. Apply the Pythagorean Theorem and similar triangles as needed to find the length of AD¯¯¯¯¯¯¯¯
. Round the answer to two decimal places.

Answer 1

Let's denote the length of AD as x.

Since ABC is a right triangle, we can apply the Pythagorean theorem:
AC^2 + BC^2 = AB^2

Let's denote the length of AC as a and the length of BC as b:

a^2 + b^2 = AB^2

Since AD is the altitude of triangle ABC, we can use similar triangles to relate the lengths of AD, CD, and AC:

AD/CD = AC/BC

Substituting the value of AD as x and CD as a, we get:

x/a = a/b

Cross-multiplying, we get:

x * b = a^2

Now, let's substitute the value of a from the Pythagorean theorem equation:

x * b = (AB^2 - b^2)

Simplifying:

x * b = AB^2 - b^2

Now, let's isolate x:

x = (AB^2 - b^2)/b

Using the Pythagorean theorem, we know that AB^2 = AC^2 + BC^2:

x = (AC^2 + BC^2 - b^2)/b

Since AC and BC are the legs of the right triangle, we can substitute their values as needed.

Finally, if you provide the values for AC, BC, and b, we can calculate the length of AD by substituting those values into the formula and rounding the answer to two decimal places.

Answer 2

so what are the two decimal places

Answer 3

I apologize for the confusion. In order for me to provide the specific answer rounded to two decimal places, I would need the actual values for AC, BC, and b. Please provide those values so that I can calculate the length of AD and round it correctly.