Question

What is the length of the unknown leg in the right triangle?

A right triangle has a side with length StartRoot 23 EndRoot yards and hypotenuse with length StartRoot 87 EndRoot yards
8 yd
StartRoot 110 EndRoot yd
64 yd
StartRoot 7040 EndRoot yd

Answer 1

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

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

where \( a \) and \( b \) are the lengths of the legs, and \( c \) is the length of the hypotenuse.

In this case, we have:

- One leg \( a = \sqrt{23} \) yards
- Hypotenuse \( c = \sqrt{87} \) yards

We need to find the unknown leg \( b \).

Using the Pythagorean theorem, we can rearrange the equation to solve for \( b \):

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

Substituting the given values:

\[
b^2 = (\sqrt{87})^2 - (\sqrt{23})^2
\]

Calculating the squares:

\[
b^2 = 87 - 23
\]
\[
b^2 = 64
\]

Now, taking the square root of both sides:

\[
b = \sqrt{64} = 8 \text{ yards}
\]

Therefore, the length of the unknown leg is \( \boxed{8} \) yards.