Final answer:
The length of the diagonal of Tom's rectangular mirror is found using the Pythagorean theorem. By squaring the lengths of the two sides (38 inches and 30 inches), adding them together, and then taking the square root, we determine that the diagonal is approximately 48.4 inches.
Step-by-step explanation:
To find the length of the diagonal of Tom's mirror, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Assuming the mirror is rectangular, the two sides given are perpendicular, so we can treat them as the legs of a right-angled triangle, with the diagonal as the hypotenuse.
The formula is:
c^2 = a^2 + b^2
Where c is the hypotenuse, and a and b are the other two sides of the triangle. Substituting the given values:
c^2 = 38^2 + 30^2
c^2 = 1444 + 900
c^2 = 2344
Now we find the square root to solve for c:
c = √2344
c ≈ 48.4 inches
Therefore, the length of the diagonal of the mirror is approximately 48.4 inches.