Find the measure of side b

To find the measure of side b, we need to use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the Pythagorean theorem can be represented as:

a^2 + b^2 = c^2

Given that side a is 3 inches and side c is 10 inches, we can substitute these values into the formula:

3^2 + b^2 = 10^2
9 + b^2 = 100

Now, we can solve for b:

b^2 = 100 - 9
b^2 = 91

Taking the square root of both sides to solve for b:

b = √91

Therefore, the measure of side b is approximately 9.54 inches.