Question

A right triangle has a leg length of square root of 7 and a hypotenuse length of 4. Determine the length of the other leg of the right triangle.

square root of 57
square root of 49
8
3

Answer 1

To determine the length of the other leg of the right triangle, we can use the Pythagorean theorem, which states that in a right triangle:

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

where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the legs. In this case, we know one leg \(a = \sqrt{7}\) and the hypotenuse \(c = 4\). We need to find the length of the other leg \(b\).

First, we calculate \(c^2\):

\[
c^2 = 4^2 = 16
\]

Next, we calculate \(a^2\):

\[
a^2 = (\sqrt{7})^2 = 7
\]

Now we can substitute \(a\) and \(c\) into the Pythagorean theorem:

\[
\sqrt{7}^2 + b^2 = 4^2
\]

This gives us:

\[
7 + b^2 = 16
\]

Next, we isolate \(b^2\):

\[
b^2 = 16 - 7
\]

\[
b^2 = 9
\]

Now we take the square root of both sides to find \(b\):

\[
b = \sqrt{9} = 3
\]

Thus, the length of the other leg of the right triangle is \(3\).

The correct answer is \(3\).