Question
find the values of x and y on the 45 45 90 degree special right triangle.
image shows right triangle with 45 degrees in both corners and the opposite side with an 8
image shows right triangle with 45 degrees in both corners and the opposite side with an 8
Answers
GPT-4o mini
In a 45-45-90 triangle, the sides are in a specific ratio: the legs are equal, and the length of the hypotenuse is \(\sqrt{2}\) times the length of each leg.
Given that the length of the legs (the two sides opposite the 45° angles) are equal, we can denote the length of each leg as \(x\).
From the information provided, if the opposite side (which corresponds to the legs in this case) measures 8, we have:
\[
x = 8
\]
Now, to find the length of the hypotenuse \(y\), we can use the 45-45-90 triangle relationship:
\[
y = x\sqrt{2}
\]
Substituting the value of \(x\):
\[
y = 8\sqrt{2}
\]
Thus, in the 45-45-90 triangle with each leg measuring 8, the values of \(x\) and \(y\) are:
\[
x = 8 \quad \text{and} \quad y = 8\sqrt{2}
\]
Given that the length of the legs (the two sides opposite the 45° angles) are equal, we can denote the length of each leg as \(x\).
From the information provided, if the opposite side (which corresponds to the legs in this case) measures 8, we have:
\[
x = 8
\]
Now, to find the length of the hypotenuse \(y\), we can use the 45-45-90 triangle relationship:
\[
y = x\sqrt{2}
\]
Substituting the value of \(x\):
\[
y = 8\sqrt{2}
\]
Thus, in the 45-45-90 triangle with each leg measuring 8, the values of \(x\) and \(y\) are:
\[
x = 8 \quad \text{and} \quad y = 8\sqrt{2}
\]