Question

part 1 of 4
the length of the hypotenuse, c, is 11 m. if we call the other known side a we know that a = 10 m.
we will use the pythagorean theorem to find the unknown side, b.

part 2 of 4
substitute 10 for a and 11 for c into the equation given by the pythagorean theorem and simplify the squares.
$a^2 + b^2 = c^2$
$10^2 + b^2 = 11^2$
$100 + b^2 = 121$

part 3 of 4
solve for b. use a calculator if necessary. (round your answer to one decimal place.)
$100 + b^2 = 121$
$b^2 = 121 - 100$
$b^2 = \square$
$\sqrt{b^2} = \sqrt{\square}$
$b = \square$

Explanation:

Step1: Calculate \( b^2 \)

We have the equation \( b^2 = 121 - 100 \). Subtracting these values, we get \( b^2 = 21 \).

Step2: Take the square root of both sides

To solve for \( b \), we take the square root of both sides: \( \sqrt{b^2} = \sqrt{21} \). Since \( \sqrt{b^2} = b \) (for \( b \geq 0 \), as it represents a length), we have \( b = \sqrt{21} \). Calculating \( \sqrt{21} \) (using a calculator), we get approximately \( 4.6 \) (rounded to one decimal place).

Answer:

First blank (for \( b^2 \)): \( 21 \)
Second blank (inside the square root): \( 21 \)
Third blank (for \( b \)): \( 4.6 \)