In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a=5.9 feet and b=6.9 feet, what is c? If necessary, round to the nearest tenth.c=feet

1 answer

To find the length of the hypotenuse \( c \) in a right triangle with legs \( a \) and \( b \), you can use the Pythagorean theorem, which states:

\[ c^2 = a^2 + b^2 \]

Substituting the given values of \( a \) and \( b \):

\[ c^2 = (5.9)^2 + (6.9)^2 \]

Calculating \( (5.9)^2 \):

\[ (5.9)^2 = 34.81 \]

Calculating \( (6.9)^2 \):

\[ (6.9)^2 = 47.61 \]

Now, add these two results:

\[ c^2 = 34.81 + 47.61 = 82.42 \]

To find \( c \), take the square root of \( c^2 \):

\[ c = \sqrt{82.42} \approx 9.1 \]

Therefore, the length of the hypotenuse \( c \) is approximately:

\[ \boxed{9.1} \text{ feet} \]