To find the length of the other leg (labeled \( x \)) in a right triangle, we can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the hypotenuse, and \( a \) and \( b \) are the legs of the triangle. In this case, we can denote the known leg as \( a = 11.9 \) km, the hypotenuse as \( c = 14.7 \) km, and the unknown leg as \( b = x \).
Plugging the known values into the equation:
\[ (11.9)^2 + x^2 = (14.7)^2 \]
Calculating \( (11.9)^2 \):
\[ 11.9^2 = 141.61 \]
Calculating \( (14.7)^2 \):
\[ 14.7^2 = 216.09 \]
Now we can substitute these values back into the Pythagorean theorem:
\[ 141.61 + x^2 = 216.09 \]
Now solve for \( x^2 \):
\[ x^2 = 216.09 - 141.61 \]
\[ x^2 = 74.48 \]
Now, find \( x \) by taking the square root of both sides:
\[ x = \sqrt{74.48} \approx 8.634 \]
Rounding to the nearest tenth gives:
\[ x \approx 8.6 \text{ km} \]
So, the length of the other leg \( x \) is approximately 8.6 km.
1 answer