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Special Right Triangles Quick Check 3 of 53 of 5 Items Question What is the length of the hypotenuse of a 30-60-90 triangle if the side opposite the 60-degree angle is 63–√ ?(1 point) Responses 123–√ 12 Start Root 3 End Root 6 6 23–√ 2 Start Root 3 End Root 12 12 Skip to navigation page 15 of 15
Answers
GPT-4o mini
In a 30-60-90 triangle, the side lengths are in a specific ratio:
- The side opposite the 30-degree angle (the shortest side) is \( x \).
- The side opposite the 60-degree angle is \( x\sqrt{3} \).
- The hypotenuse (the side opposite the 90-degree angle) is \( 2x \).
In this question, you mentioned that the side opposite the 60-degree angle is \( 63\sqrt{} \). Assuming this means \( 63\sqrt{3}\), we can set \( x\sqrt{3} = 63\sqrt{3} \).
To find \( x \):
\[
x\sqrt{3} = 63\sqrt{3}
\]
Dividing both sides by \( \sqrt{3} \):
\[
x = 63
\]
Now we can find the hypotenuse, which is \( 2x \):
\[
\text{Hypotenuse} = 2x = 2 \cdot 63 = 126
\]
Therefore, the length of the hypotenuse is **126**.
- The side opposite the 30-degree angle (the shortest side) is \( x \).
- The side opposite the 60-degree angle is \( x\sqrt{3} \).
- The hypotenuse (the side opposite the 90-degree angle) is \( 2x \).
In this question, you mentioned that the side opposite the 60-degree angle is \( 63\sqrt{} \). Assuming this means \( 63\sqrt{3}\), we can set \( x\sqrt{3} = 63\sqrt{3} \).
To find \( x \):
\[
x\sqrt{3} = 63\sqrt{3}
\]
Dividing both sides by \( \sqrt{3} \):
\[
x = 63
\]
Now we can find the hypotenuse, which is \( 2x \):
\[
\text{Hypotenuse} = 2x = 2 \cdot 63 = 126
\]
Therefore, the length of the hypotenuse is **126**.