In a right triangle, you can use the Pythagorean theorem to find the length of the hypotenuse. The theorem states that:
\[ c^2 = a^2 + b^2 \]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the other two sides.
In your case, the left side (one leg of the triangle) is \( 4 \) and the top side (the other leg) is \( 7 \).
- Substitute the values into the formula:
\[ c^2 = 4^2 + 7^2 \]
- Calculate the squares:
\[ c^2 = 16 + 49 \] \[ c^2 = 65 \]
- Take the square root of both sides to find \( c \):
\[ c = \sqrt{65} \]
Now, to estimate \( \sqrt{65} \) to two decimal places:
Using a calculator or estimating the square root, we find:
\[ \sqrt{65} \approx 8.06 \]
So, the length of the missing hypotenuse is approximately 8.06.