Final answer:
By using the properties of similar triangles and setting up a ratio of the stick's height to its shadow length, which is equal to the building's height to its shadow length, we can calculate the height of the building to be approximately 18.46 meters.
Step-by-step explanation:
To solve for the height of the building, we can use the properties of similar triangles. The stick and its shadow form one triangle, and the building and its shadow form another. Since these triangles are similar, the ratios of corresponding sides are equal.
The stick is 1 meter tall and casts a shadow 1.3 meters long. Therefore, the ratio of the height to the shadow length for the stick is 1/1.3.
The building casts a 24-meter-long shadow, and we want to find the height (h) of the building. Setting up a proportion based on the similar triangles, we have 1/1.3 = h/24.
By solving this proportion for h, we get h = 24/1.3, which equals approximately 18.46 meters when rounded to two decimal places. Therefore, the building is approximately 18.46 meters tall.