Question

A 2.5 meter stick casts a 3.2 meter shadow. How tall is a nearby building that casts a shadow that is 19.2 meters long?

a) 15 meters
b) 20 meters
c) 25 meters
d) 30 meters

Answer 1

To determine the height of the building, we use similar triangles and set up a proportion between the stick and its shadow and the building and its shadow. Upon solving, the height of the building is found to be 15 meters.

Step-by-step explanation:

For problems like this, we use similar triangles because the sun's rays, which cause the shadows, are parallel. This creates two similar triangles, one with the stick and its shadow, and one with the building and its shadow. To solve for the height of the building, we can set up a proportion using the height and shadow length of the stick: height of stick/shadow of stick = height of building/shadow of the building. Now we can plug in the values you provided: 2.5 m / 3.2 m = height of building / 19.2 m. With cross multiplication, we find the height of the building: 2.5 m * 19.2 m = height of building * 3.2 m. height of building = (2.5 m * 19.2 m) / 3.2 m. Upon calculating, we get the height of the building = 15 m. Therefore, the correct answer is (a) 15 meters.