Question
What is the length of the hypotenuse of a 30-60-90 triangle if the side opposite the 60-degree angle is 63–√
Answers
GPT-4o mini
In a 30-60-90 triangle, the sides are in a specific ratio: the side opposite the 30-degree angle is \( x \), the side opposite the 60-degree angle is \( x\sqrt{3} \), and the hypotenuse is \( 2x \).
Given that the side opposite the 60-degree angle is \( 63\sqrt{3} \), we can set up the equation:
\[
x\sqrt{3} = 63\sqrt{3}
\]
From this, we can solve for \( x \):
\[
x = 63
\]
Now we can find the length of the hypotenuse, which is given by \( 2x \):
\[
\text{Hypotenuse} = 2x = 2 \times 63 = 126
\]
Therefore, the length of the hypotenuse is \( \boxed{126} \).
Given that the side opposite the 60-degree angle is \( 63\sqrt{3} \), we can set up the equation:
\[
x\sqrt{3} = 63\sqrt{3}
\]
From this, we can solve for \( x \):
\[
x = 63
\]
Now we can find the length of the hypotenuse, which is given by \( 2x \):
\[
\text{Hypotenuse} = 2x = 2 \times 63 = 126
\]
Therefore, the length of the hypotenuse is \( \boxed{126} \).