Question

find the length of the missing side for this right triangle.
right side= 4
hypotenuse=9
top=?

Answer 1

To find the length of the missing side (the top side) 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 other two sides.

In this case:
- The length of the right side \( a = 4 \)
- The length of the hypotenuse \( c = 9 \)
- We need to find the length of the top side \( b \).

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

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

Substituting the given values:

\[ b^2 = 9^2 - 4^2 \]
\[ b^2 = 81 - 16 \]
\[ b^2 = 65 \]

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

\[ b = \sqrt{65} \]

Thus, the length of the missing side (the top side) is \( \sqrt{65} \), which is approximately \( 8.06 \).