Question

If on leg on a triangle is 11.9 km the hypotenuse is 14.7 km and the other leg is labeled x what does x equal round to the nearest tenth if necessary

Answer 1

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**.