Question

1. a=□ b=6 c=10

Explanation:

Assuming this is a right - triangle problem where \(c\) is the hypotenuse and \(a\), \(b\) are the legs, we can use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) to solve for \(a\).

Step 1: Recall the Pythagorean theorem

The Pythagorean theorem states that for a right - triangle with legs of length \(a\) and \(b\) and hypotenuse of length \(c\), the relationship is given by \(a^{2}+b^{2}=c^{2}\). We want to solve for \(a\), so we can re - arrange the formula to \(a^{2}=c^{2}-b^{2}\).

Step 2: Substitute the given values of \(b\) and \(c\)

We know that \(b = 6\) and \(c = 10\). Substitute these values into the formula \(a^{2}=c^{2}-b^{2}\):
\[

$$\begin{align*} a^{2}&=10^{2}-6^{2}\\ a^{2}&=100 - 36\\ a^{2}&=64 \end{align*}$$

\]

Step 3: Solve for \(a\)

To find the value of \(a\), we take the square root of both sides of the equation \(a^{2}=64\). Since \(a\) represents the length of a side of a triangle, we take the positive square root (because length cannot be negative). So \(a=\sqrt{64}=8\).

Answer:

\(a = 8\)