In a right triangle, $a$ and $b$ are the lengths of the legs and $c$ is the length of the hypotenuse. Given that $b = 72$ millimeters and $c = 78$ millimeters, we need to find the length of $a$ and round it to the nearest tenth.

1. Problem Description

In a right triangle, $a$ and $b$ are the lengths of the legs and $c$ is the length of the hypotenuse. Given that $b = 72$ millimeters and $c = 78$ millimeters, we need to find the length of $a$ and round it to the nearest tenth.

2. Solution Steps

We can use the Pythagorean theorem to solve for $a$. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse ($c$) is equal to the sum of the squares of the lengths of the other two sides ($a$ and $b$). The formula is:

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

We are given $b = 72$ and $c = 78$. We can plug these values into the formula and solve for $a$:

$a^2 + (72)^2 = (78)^2$

$a^2 + 5184 = 6084$

$a^2 = 6084 - 5184$

$a^2 = 900$

$a = \sqrt{900}$

$a = 30$

3. Final Answer

a = 30.0 millimeters