Question

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

Answer 1

To find the length of the missing side of the right triangle, we can use the Pythagorean theorem, which states:

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

where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the other two sides. In this case, we know:

- The height (one leg) = 4
- The hypotenuse = 9
- The length (the other leg) = \( x \)

We can set up the equation:

\[ 4^2 + x^2 = 9^2 \]

Calculating the squares:

\[ 16 + x^2 = 81 \]

Now, isolate \( x^2 \):

\[ x^2 = 81 - 16 \]
\[ x^2 = 65 \]

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

\[ x = \sqrt{65} \]

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