Question

Give is the right triangle ABC height of 3 DB=4 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

In right triangle \( ABC \), we have the following information: the height \( CD \) is given as \( 3 \) and \( DB \) is given as \( 4 \). We want to find the length of \( AD \).

From the problem setup, we'll assume:

- \( D \) is the foot of the altitude \( CD \) from vertex \( C \) to hypotenuse \( AB \).
- \( AD \) and \( DB \) are segments of the hypotenuse \( AB \).

According to the properties of similar triangles, when an altitude is drawn to the hypotenuse of a right triangle, it creates two smaller right triangles that are similar to each other and to the original triangle.

Let:

- \( AD = x \)
- \( DB = 4 \)

According to the property of the altitude in a right triangle:

\[
CD^2 = AD \times DB
\]
\[
3^2 = x \times 4
\]
\[
9 = 4x
\]
\[
x = \frac{9}{4}
\]
\[
x = 2.25
\]

Thus, the length of \( AD \) is:

\[
AD = 2.25
\]

Rounded to two decimal places, the length of \( AD \) is:

\[
\boxed{2.25}
\]