Question

there is a right triangle labeled XYZ, and there is a line going horizontally through it labeled AB, creating another right triangle in the right triangle XYZ, so the smaller one, inside of XYZ is labeled AYB.

If triangle XYZ - AYB, and line XY = 24 yards, line YZ = 30 yards, and line YA= 8 yards, then what is the length of line YB?

Answer 1

A. 10 yards
B. 15 yards
C. 25 yards
D. 12 yards

Answer 2

To find the length of line YB in triangle AYB, we can first apply the Pythagorean theorem to find the length of line XZ in triangle XYZ.

We have:
- XY = 24 yards
- YZ = 30 yards

Using the Pythagorean theorem, we can calculate the length of the hypotenuse (XZ):

\[
XZ = \sqrt{XY^2 + YZ^2}
\]

Calculating it:

\[
XZ = \sqrt{(24)^2 + (30)^2} = \sqrt{576 + 900} = \sqrt{1476}
\]
\[
XZ \approx 38.4 \text{ yards}
\]

Next, we know that line YA is part of line YZ. Given that YA = 8 yards, we can find line YB:

Since YZ is 30 yards and YA is 8 yards, we have:

\[
YB = YZ - YA
\]
\[
YB = 30 - 8 = 22 \text{ yards}
\]

Thus, the length of line YB is 22 yards.