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.

Tags

CCSS.HSG.SRT.A.2

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.

Tags

CCSS.HSG.SRT.B.5

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

Tags

CCSS.7.G.A.1

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

Tags

CCSS.HSG.SRT.B.5

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

Tags

CCSS.HSG.SRT.A.2

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

Tags

CCSS.HSG.SRT.B.4

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

Tags

CCSS.7.G.A.1

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

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6