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 3.5
In a 30-60-90 triangle, the ratio of the lengths of the sides is 1:√3:2.
In this case, the side opposite the 60-degree angle is given as 63–√ , which can be simplified to 63 - √3.
Thus, the hypotenuse, which is twice the length of the side opposite the 30-degree angle, is 2(63 - √3) = 126 - 2√3.
Therefore, the length of the hypotenuse is 126 - 2√3.
In this case, the side opposite the 60-degree angle is given as 63–√ , which can be simplified to 63 - √3.
Thus, the hypotenuse, which is twice the length of the side opposite the 30-degree angle, is 2(63 - √3) = 126 - 2√3.
Therefore, the length of the hypotenuse is 126 - 2√3.