A 32-m tall building casts a shadow. The distance from the top of the building to the tip of the shadow is 35m. Find the length of the shadow. If necessary, round your answer to the nearest tenth.
From the given information, we can form a right triangle with the height of the building as the vertical leg and the length of the shadow as the horizontal leg. The distance from the top of the building to the tip of the shadow is the hypotenuse.
Using the Pythagorean theorem, we have:
$(\text{Length of shadow})^2 + (32\, \text{m})^2 = (35\, \text{m})^2$
Simplifying the equation, we get:
$(\text{Length of shadow})^2 = (35^2) - (32^2)$
$(\text{Length of shadow})^2 = 1225 - 1024$
$(\text{Length of shadow})^2 = 201$
Taking the square root of both sides, we find:
$\text{Length of shadow} = \sqrt{201} \approx \boxed{14.2 \text{ m}}$