Question

note: triangle may not be drawn to scale. suppose b = 9 find exact values for the other sides. a = c =

Explanation:

Step1: Identify Triangle Type

The triangle is a right - isosceles triangle (two angles are \(45^{\circ}\), one is \(90^{\circ}\)), so the two legs (\(a\) and \(b\)) are equal. Given \(b = 9\), so \(a=b = 9\).

Step2: Use Pythagorean Theorem for \(c\)

For a right - triangle, \(c=\sqrt{a^{2}+b^{2}}\). Substitute \(a = 9\) and \(b = 9\):
\(c=\sqrt{9^{2}+9^{2}}=\sqrt{81 + 81}=\sqrt{162}=\sqrt{81\times2}=9\sqrt{2}\)

Answer:

\(a = 9\)
\(c = 9\sqrt{2}\)