In a right triangle, \( a \) and \( b \) are the lengths of the legs and \( c \) is the length of the hypotenuse. If \( a=1.4 \) feet and \( b=6 \) feet, what is \( c \) ? If necessary, round to the nearest tenth. \( c= \)

To find the length of the hypotenuse \( c \) in a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Given: - Length of one leg, \( a = 1.4 \) feet - Length of the other leg, \( b = 6 \) feet We can use the Pythagorean theorem to find the length of the hypotenuse \( c \): \[ c^2 = a^2 + b^2 \] Substitute the given values: \[ c^2 = 1.4^2 + 6^2 \] \[ c^2 = 1.96 + 36 \] \[ c^2 = 37.96 \] Now, we need to find the square root of \( 37.96 \) to get the length of the hypotenuse \( c \): \[ c = \sqrt{37.96} \] Let's calculate the value of \( c \) and round it to the nearest tenth. Calculate the value by following steps: - step0: Calculate: \(\sqrt{37.96}\) - step1: Rewrite the expression: \(\sqrt{\frac{949}{25}}\) - step2: Use the properties of radicals: \(\frac{\sqrt{949}}{\sqrt{25}}\) - step3: Simplify the expression: \(\frac{\sqrt{949}}{5}\) The length of the hypotenuse \( c \) is approximately 6.161 feet. Rounding to the nearest tenth, \( c \approx 6.2 \) feet.