In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a=3.4 kilometers and b=1.8 kilometers, what is c? If necessary, round to the nearest tenth.

1 answer

To find the length of the hypotenuse \( c \) in a right triangle with legs \( a \) and \( b \), you can use the Pythagorean theorem, which states:

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

Given:

  • \( a = 3.4 \) kilometers
  • \( b = 1.8 \) kilometers

First, we need to calculate \( a^2 \) and \( b^2 \):

\[ a^2 = (3.4)^2 = 11.56 \] \[ b^2 = (1.8)^2 = 3.24 \]

Now, add these two values:

\[ c^2 = a^2 + b^2 = 11.56 + 3.24 = 14.8 \]

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

\[ c = \sqrt{14.8} \approx 3.844 \]

Finally, round to the nearest tenth:

\[ c \approx 3.8 \text{ kilometers} \]

Therefore, the length of the hypotenuse \( c \) is approximately 3.8 kilometers.