What is the length of the hypotenuse? If necessary, round to the nearest tenth. a = 8.5 b = 4.2

1 answer

To find the length of the hypotenuse \( c \) of a right triangle, we can use the Pythagorean theorem:

\[ c = \sqrt{a^2 + b^2} \]

Given the side lengths \( a = 8.5 \) and \( b = 4.2 \):

\[ c = \sqrt{(8.5)^2 + (4.2)^2} \]

First, calculate \( (8.5)^2 \) and \( (4.2)^2 \):

\[ (8.5)^2 = 72.25 \] \[ (4.2)^2 = 17.64 \]

Now, add these two results together:

\[ c = \sqrt{72.25 + 17.64} = \sqrt{89.89} \]

Now calculate the square root:

\[ c \approx 9.5 \]

Therefore, the length of the hypotenuse rounded to the nearest tenth is \( \boxed{9.5} \).