find the length of the missing side for this right triangle.

Question

left side=?
top side=5
bottom side=4

Answer 1

In a right triangle, you can use the Pythagorean theorem to find the length of the missing side. The theorem states that:

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

where \(c\) is the length of the hypotenuse and \(a\) and \(b\) are the lengths of the other two sides.

In your case, the top side is 5 (which we will assume is one of the legs, \(b\)) and the bottom side is 4 (which we will assume is the other leg, \(a\)). We want to find the hypotenuse \(c\).

Using the Pythagorean theorem:

\[ 4^2 + 5^2 = c^2 \]

Calculating the squares:

\[ 16 + 25 = c^2 \]

Adding the values together:

\[ 41 = c^2 \]

Now, taking the square root of both sides to find \(c\):

\[ c = \sqrt{41} \]

So, the length of the hypotenuse is approximately 6.4.

Answer 2

incorrect the answer is NOT 6.4

Answer 3

I apologize for the confusion. Let's clarify the problem. You mentioned a right triangle with a "left side" (which I assume you're asking for), a "top side" of 5, and a "bottom side" of 4.

If the bottom side (4) and the left side are the legs of the triangle and the top side (5) is the hypotenuse, we can set it up as follows:

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

Where \(a = 4\), \(b\) is the missing side (the left side), and \(c = 5\).

Plugging in the values we have:

\[ 4^2 + b^2 = 5^2 \]

Calculating the squares:

\[ 16 + b^2 = 25 \]

Subtracting 16 from both sides:

\[ b^2 = 25 - 16 \]

\[ b^2 = 9 \]

Now taking the square root of both sides:

\[ b = \sqrt{9} \] \[ b = 3 \]

So, the length of the missing side (left side) is 3. Thank you for your patience, and I apologize for the earlier oversight.