Question
A right triangle with the lengths of 30 and 90.
what is the hypotenuse?
what is the hypotenuse?
Answers
GPT-4o mini
To find the hypotenuse of a right triangle when you have the lengths of the two legs, you can use the Pythagorean theorem, which states:
\[ c^2 = a^2 + b^2 \]
where \( c \) is the hypotenuse, and \( a \) and \( b \) are the lengths of the other two sides.
Given that the lengths of the two legs are 30 and 90, we can substitute into the formula:
\[ c^2 = 30^2 + 90^2 \]
\[ c^2 = 900 + 8100 \]
\[ c^2 = 9000 \]
Now, take the square root of both sides to find \( c \):
\[ c = \sqrt{9000} \]
\[ c = \sqrt{100 \times 90} \]
\[ c = 10\sqrt{90} \]
\[ c \approx 10 \times 9.4868 \] (since \(\sqrt{90} \approx 9.4868\))
\[ c \approx 94.868 \]
Thus, the hypotenuse is approximately \( 94.87 \).
\[ c^2 = a^2 + b^2 \]
where \( c \) is the hypotenuse, and \( a \) and \( b \) are the lengths of the other two sides.
Given that the lengths of the two legs are 30 and 90, we can substitute into the formula:
\[ c^2 = 30^2 + 90^2 \]
\[ c^2 = 900 + 8100 \]
\[ c^2 = 9000 \]
Now, take the square root of both sides to find \( c \):
\[ c = \sqrt{9000} \]
\[ c = \sqrt{100 \times 90} \]
\[ c = 10\sqrt{90} \]
\[ c \approx 10 \times 9.4868 \] (since \(\sqrt{90} \approx 9.4868\))
\[ c \approx 94.868 \]
Thus, the hypotenuse is approximately \( 94.87 \).