Question

8 a = __ , b = __

Explanation:

Step1: Apply the Pythagorean theorem for the first triangle

For the first right - triangle with legs 3.1 and 5.5, by the Pythagorean theorem \(a^{2}=3.1^{2}+5.5^{2}\).
\[a^{2}=9.61 + 30.25=39.86\]
\[a=\sqrt{39.86}\approx 6.31\]

Step2: Apply the Pythagorean theorem for the second triangle

For the second right - triangle with one leg 2.7 and hypotenuse 5.5, by the Pythagorean theorem \(b^{2}=5.5^{2}-2.7^{2}\).
\[b^{2}=30.25 - 7.29 = 22.96\]
\[b=\sqrt{22.96}\approx4.79\]

Answer:

\(a\approx6.31\), \(b\approx4.79\)