Question

What is the length of the unknown leg of the right​ triangle?
2 ft
1 ft
​(The figure is not drawn to​ scale.)
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Part 1
The length of the unknown leg of the right triangle is
  
enter your response here ft.
​(Round to one decimal place as​ needed.)

Answer 1

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

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

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

From your description, it seems we know one leg is 2 ft, and the other leg is 1 ft. If we are finding the hypotenuse, we can plug in those values:

Let \( a = 1 \) ft, \( b = 2 \) ft, and we are looking for \( c \).

\[
1^2 + 2^2 = c^2
\]
\[
1 + 4 = c^2
\]
\[
5 = c^2
\]
\[
c = \sqrt{5} \approx 2.2 \text{ ft}
\]

If you're looking for the other leg (let's assume we know the hypotenuse is longer), we can denote the unknown leg as \( x \):

Given that the hypotenuse is 2 ft, we can write:

\[
x^2 + 1^2 = 2^2
\]
\[
x^2 + 1 = 4
\]
\[
x^2 = 4 - 1
\]
\[
x^2 = 3
\]
\[
x = \sqrt{3} \approx 1.7 \text{ ft}
\]

If you need a specific calculation or interpretation, please clarify!