Final answer:
Using the concept of similar triangles, we set up a proportion with the man's height and shadow compared to the water tower's height and shadow. After cross-multiplication and division, we determine that the height of the water tower is 156 feet.
Step-by-step explanation:
To solve the question, we will use the concept of similar triangles. The situation presents two similar triangles: one formed by the 6-foot tall man and his 1.5-foot shadow, and the other formed by the water tower and its 39-foot shadow. The reason these triangles are similar is because the sun's rays, which are parallel, create corresponding angles of elevation that are equal. To find the height of the water tower, we can set up a proportion based on the similar triangles.
Let's denote the unknown height of the water tower as 'h'. Then the proportion becomes:
Man's height / Man's shadow = Water tower's height / Water tower's shadow
Now we plug in the known values:
6 ft / 1.5 ft = h / 39 ft
By cross-multiplying to solve for 'h', we get:
6 ft × 39 ft = 1.5 ft × h
234 ft² = 1.5 ft × h
To find 'h', we divide both sides by 1.5 ft:
h = 234 ft² / 1.5 ft
h = 156 ft
Therefore, the height of the water tower is 156 feet.