What is b?

To find the length of leg b in a right triangle where you know the lengths of leg a and the hypotenuse c, you can use the Pythagorean theorem, which states:

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

Given:

– ( a = 2 ) yards

– ( c = 3 ) yards

Now, plug in the values:

[ (2)^2 + b^2 = (3)^2 ]

This simplifies to:

[ 4 + b^2 = 9 ]

Now, subtract 4 from both sides:

[ b^2 = 9 – 4 ]

[ b^2 = 5 ]

Next, take the square root of both sides to find b:

[ b = sqrt{5} ]

Calculating that gives:

[ b approx 2.236 ]

Rounding to the nearest tenth:

[ b approx 2.2 ]

So, the length of b is approximately 2.2 yards.