Final answer:
To find the height of the Space Needle, a proportion is set up comparing the woman's height and shadow length to the Space Needle's shadow length. The calculation reveals that the Space Needle is approximately 60.83 feet tall.
Step-by-step explanation:
The student is asking to solve a proportion problem to determine the height of the Space Needle in Seattle, Washington. This is based on the concept of similar triangles where two figures have the same shape but different sizes, and the sides are in proportion. Since the woman who is 5'5" (which is equivalent to 65 inches) tall casts a 13-inch shadow, we can set up a proportion where the height of the Space Needle is to its shadow (121 feet or 1452 inches) as the woman's height is to her shadow. The proportion looks like this:
Height of Space Needle / 1452 inches = 65 inches / 13 inches
By cross-multiplication, we can solve for the height of the Space Needle:
Height of Space Needle * 13 inches = 65 inches * 1452 inches
Height of Space Needle = (65 * 1452) / 13
Height of Space Needle = 9490 / 13
Height of Space Needle = 730 inches
To convert this back to feet, we divide by 12, since there are 12 inches in a foot:
Height of Space Needle = 730 inches / 12 inches/foot = 60.83 feet (approximately)
Therefore, the Space Needle is approximately 60.83 feet tall, based on the given shadows and the woman's height.