Question

Find the missing lengths. Round to the nearest tenth.

The hypotenuse of the right triangle is seven while the shorter leg is four. What's the longer leg? No decimals

Answer 1

To find the length of the longer leg of a 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 your case, the hypotenuse \( c \) is 7, and one leg \( a \) is 4. We need to find the other leg \( b \).

Using the Pythagorean theorem:

\[
4^2 + b^2 = 7^2
\]

Calculating the squares:

\[
16 + b^2 = 49
\]

Now, we can solve for \( b^2 \):

\[
b^2 = 49 - 16
\]

\[
b^2 = 33
\]

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

\[
b = \sqrt{33}
\]

To find the value of \( \sqrt{33} \) rounded to the nearest tenth, we can estimate:

\[
\sqrt{33} \approx 5.744
\]

Rounding to the nearest tenth gives us:

\[
b \approx 5.7
\]

So, the length of the longer leg is approximately **5.7** (rounded to the nearest tenth).