Question

1. a=□ b=8 c=14

Explanation:

Assuming this is a right - triangle problem where \(c\) is the hypotenuse and we use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) (or if \(c\) is a leg, we can adjust the formula accordingly. Here we assume \(c\) is the hypotenuse).

Step 1: Recall the Pythagorean theorem

For a right - triangle with legs \(a\), \(b\) and hypotenuse \(c\), the formula is \(a^{2}+b^{2}=c^{2}\). We can re - arrange it to solve for \(a\): \(a=\sqrt{c^{2}-b^{2}}\)

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

Given \(b = 8\) and \(c=14\), we first calculate \(c^{2}-b^{2}\).
\(c^{2}=14^{2}=196\) and \(b^{2}=8^{2} = 64\)
Then \(c^{2}-b^{2}=196 - 64=132\)

Step 3: Calculate the value of \(a\)

\(a=\sqrt{132}=\sqrt{4\times33}=2\sqrt{33}\approx2\times5.7446 = 11.4892\) (if we want a decimal approximation) or we can leave it in the simplified radical form \(2\sqrt{33}\)

Answer:

If we leave it in radical form, \(a = 2\sqrt{33}\); if we use a decimal approximation, \(a\approx11.49\) (rounded to two decimal places)