Question
What is the missing side length x?
Imagine a right triangle. At the left slanted line is "5 * sqrt 2", on the right line is y, and the bottom line is labelled x. At the top point of the triangle, inside of it, is 45 degrees.
Imagine a right triangle. At the left slanted line is "5 * sqrt 2", on the right line is y, and the bottom line is labelled x. At the top point of the triangle, inside of it, is 45 degrees.
Answers
Answered by
GPT-4o mini
In a right triangle with a 45-degree angle, we have an isosceles right triangle where the two legs (the shorter sides) are of equal length. If the length of each leg is \( y \), then the hypotenuse, which is opposite the right angle, can be found using the relationship:
\[
\text{Hypotenuse} = y \sqrt{2}
\]
In your case, the hypotenuse is given as \( 5 \sqrt{2} \). Therefore, we can set up the equation:
\[
y \sqrt{2} = 5 \sqrt{2}
\]
To find \( y \), we can divide both sides by \( \sqrt{2} \):
\[
y = 5
\]
Since this is an isosceles right triangle, the length of the other leg (which you have labeled as \( x \)) is equal to the length of \( y \):
\[
x = y = 5
\]
Thus, the missing side length \( x \) is:
\[
\boxed{5}
\]
\[
\text{Hypotenuse} = y \sqrt{2}
\]
In your case, the hypotenuse is given as \( 5 \sqrt{2} \). Therefore, we can set up the equation:
\[
y \sqrt{2} = 5 \sqrt{2}
\]
To find \( y \), we can divide both sides by \( \sqrt{2} \):
\[
y = 5
\]
Since this is an isosceles right triangle, the length of the other leg (which you have labeled as \( x \)) is equal to the length of \( y \):
\[
x = y = 5
\]
Thus, the missing side length \( x \) is:
\[
\boxed{5}
\]