Question

find the length of the missing side for this right triangle. Estimate an irrational answer to two decimal places

left side=4
top side=7
hypotenuse=?

Answer 1

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

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

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

In your case, the left side (one leg of the triangle) is \( 4 \) and the top side (the other leg) is \( 7 \).

1. Substitute the values into the formula:

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

2. Calculate the squares:

\[
c^2 = 16 + 49
\]
\[
c^2 = 65
\]

3. Take the square root of both sides to find \( c \):

\[
c = \sqrt{65}
\]

Now, to estimate \( \sqrt{65} \) to two decimal places:

Using a calculator or estimating the square root, we find:

\[
\sqrt{65} \approx 8.06
\]

So, the length of the missing hypotenuse is approximately **8.06**.