Question

9.8 in.
a
9.1 in.
what is the length of the missing leg? if necessary, round to the nearest tenth.
a = inches
submit

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \( c^2 = a^2 + b^2 \), where \( c \) is hypotenuse, \( a,b \) are legs. Here, \( c = 9.8 \), \( b = 9.1 \), solve for \( a \): \( a^2 = c^2 - b^2 \)

Step2: Calculate \( c^2 - b^2 \)

\( c^2 = 9.8^2 = 96.04 \), \( b^2 = 9.1^2 = 82.81 \), so \( a^2 = 96.04 - 82.81 = 13.23 \)

Step3: Find \( a \)

\( a = \sqrt{13.23} \approx 3.6 \) (rounded to nearest tenth)

Answer:

\( 3.6 \)