Final answer:
Using proportions based on the concept of similar triangles, the length of the tree's shadow is 6 feet, and the height of the statue is 8 meters.
Step-by-step explanation:
The student's questions relate to the concept of similar triangles in geometry, which is part of the Mathematics curriculum, most likely at the middle school level. Similar triangles have corresponding angles that are equal and their sides are in proportion.
Question 1:
A telephone pole is 60 feet tall and casts a shadow that is 24 feet long. A tree that is next to the telephone pole is 15 feet tall. To determine the length of the tree's shadow, we set up a proportion based on the similar triangles formed by the pole and its shadow and the tree and its shadow:
Height of pole / Length of pole's shadow = Height of tree / Length of tree's shadow
60 / 24 = 15 / x
Cross-multiply to find x:
60 * x = 15 * 24
x = (15 * 24) / 60
x = 6
So, the length of the tree's shadow is 6 feet.
Question 2:
A building with a height of 40 meters casts a shadow that is 30 meters long. A statue next to the building casts a shadow that is 6 meters long. The height of the statue (y) is found using a proportion:
Height of building / Length of building's shadow = Height of statue / Length of statue's shadow
40 / 30 = y / 6
Cross-multiply to solve for y:
40 * 6 = 30 * y
y = (40 * 6) / 30
y = 8
The height of the statue is 8 meters.