We are given a right triangle with legs $a$ and $b$, and hypotenuse $c$. We are given that $a = 2.9$ cm and $c = 7.7$ cm. We want to find the length of leg $b$.

1. Problem Description

We are given a right triangle with legs $a$ and $b$, and hypotenuse $c$. We are given that $a = 2.9$ cm and $c = 7.7$ cm. We want to find the length of leg $b$.

2. Solution Steps

We can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides (legs). That is:

$a^2 + b^2 = c^2$

We are given $a = 2.9$ and $c = 7.7$. We need to find $b$.

Substitute the given values into the Pythagorean theorem:

$(2.9)^2 + b^2 = (7.7)^2$

$8.41 + b^2 = 59.29$

Subtract 8.41 from both sides:

$b^2 = 59.29 - 8.41$

$b^2 = 50.88$

Take the square root of both sides:

$b = \sqrt{50.88}$

$b \approx 7.133$

Round to the nearest tenth:

$b \approx 7.1$

3. Final Answer

$b = 7.1$ centimeters.