Calculate Heights: Exploring Similar Triangles in Shadows

1. A tree casts a shadow of 15 feet. At the same time, a 5-foot tall person casts a shadow of 2 feet. Are the triangles formed by the tree and its shadow similar to the triangles formed by the person and their shadow?

• The triangles are similar only if the shadows are the same length.

• No, the triangles are not similar.

• Yes, the triangles are similar.

• The triangles are similar only if the tree is taller than the person.

2. If the triangles in the previous problem are similar, what is the height of the tree?

• The height of the tree is equal to the base of the triangle.

• The height of the tree is irrelevant to similar triangles.

• Height of the tree is calculated using the ratio of the similar triangles.

• The tree's height can be found using its shadow length only.

3. A model of a building is 3 feet tall and casts a shadow of 4 feet. If a real building is 12 feet tall, how long is its shadow?

• 10 feet

• 8 feet

• 16 feet

• 12 feet

4. Two similar triangles have side lengths in the ratio of 2:5. If one side of the smaller triangle is 6 cm, what is the length of the corresponding side in the larger triangle?

• 15 cm

• 18 cm

• 10 cm

• 12 cm

5. A flagpole is 10 feet tall and casts a shadow of 5 feet. A nearby lamp post casts a shadow of 8 feet. How tall is the lamp post if the triangles formed are similar?

• 16 feet

• 14 feet

• 18 feet

• 12 feet

6. In a park, a 4-foot tall statue casts a shadow of 2 feet. If a nearby tree casts a shadow of 10 feet, how tall is the tree?

• 12 feet

• 15 feet

• 20 feet

• 8 feet

7. A 6-foot tall person stands next to a building and casts a shadow of 3 feet. If the building casts a shadow of 12 feet, how tall is the building?

• 12 feet

• 24 feet

• 30 feet

• 18 feet

8. Two similar triangles have a ratio of 3:4. If the shorter triangle has a side length of 9 cm, what is the length of the corresponding side in the larger triangle?

• 10 cm

• 18 cm

• 15 cm

• 12 cm

9. A 5-foot tall plant casts a shadow of 1.5 feet. If a nearby tree casts a shadow of 6 feet, how tall is the tree?

• 20 feet

• 25 feet

• 10 feet

• 15 feet

10. A 2-meter tall statue casts a shadow of 1 meter. If a nearby tower casts a shadow of 5 meters, how tall is the tower?

• 4 meters

• 10 meters

• 8 meters

• 2 meters