Question

2.
a 10 ft.
c 6 ft.
b
b = ____________

Explanation:

Step1: Identify the formula

This is a right - triangle, so we can use the Pythagorean theorem. The Pythagorean theorem states that for a right - triangle with hypotenuse \(c\) and legs \(a\) and \(b\), \(a^{2}+b^{2}=c^{2}\). In this triangle, the hypotenuse \(c = 10\) ft, one leg \(a = 6\) ft, and we want to find the other leg \(b\). We can re - arrange the formula to solve for \(b\): \(b=\sqrt{c^{2}-a^{2}}\)

Step2: Substitute the values

Substitute \(c = 10\) and \(a = 6\) into the formula. First, calculate \(c^{2}-a^{2}\):
\(c^{2}-a^{2}=10^{2}-6^{2}=100 - 36=64\)

Step3: Calculate the square root

Then, find the square root of 64 to get \(b\):
\(b=\sqrt{64}=8\)

Answer:

\(b = 8\) ft