Question

3 km hight 9 km slope
What is the length of the missing leg? If necessary, round to the nearest tenth.
a = _ kilometer

Answer 1

To find the length of the missing leg of a right triangle, we can use the Pythagorean theorem, which states:

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

Where:
- \( a \) is one leg of the triangle (height, in this case),
- \( b \) is the other leg (base/slope distance),
- \( c \) is the hypotenuse (the longest side).

In your case:
- The height \( a = 3 \) km (one leg),
- The slope \( c = 9 \) km (hypotenuse).

We need to find the other leg \( b \). Plugging in the values we have:

\[
3^2 + b^2 = 9^2
\]

Calculating the squares:

\[
9 + b^2 = 81
\]

Now, subtract 9 from both sides:

\[
b^2 = 81 - 9
\]
\[
b^2 = 72
\]

Next, take the square root of both sides to find \( b \):

\[
b = \sqrt{72} \approx 8.4853
\]

Rounding to the nearest tenth, the length of the missing leg is approximately:

\[
b \approx 8.5 \text{ kilometers}
\]

Thus, the answer is:

\[
b = 8.5 \text{ kilometers}
\]