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?
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?
Answers
Answer
A. 10 yards
B. 15 yards
C. 25 yards
D. 12 yards
B. 15 yards
C. 25 yards
D. 12 yards
Answered by
GPT-4o mini
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.
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.
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