Missing sides of similar triangles, and shadow problems

Answer Key - Grade 8 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. Read this first

   Table (pole | tree, in m)

   Height 2 | ?, with the arrow × 4 from the pole to the tree. Both stand straight up and the sun makes the same angle for both (sketch, not to scale).

2. 1.

   Ari stands a 2 m pole in the sun. The tree's shadow is 4 times as long as the pole's shadow. How many meters tall is the tree?

   8

3. Table (stick | tower, in m)

   Height 1.5 | ?, with the arrow × 8 from the stick to the tower. Both stand straight up and the sun makes the same angle for both (sketch, not to scale).

4. 2.

   Bo stands a 1.5 m stick in the sun. The tower's shadow is 8 times as long as the stick's shadow. How many meters tall is the tower?

   12

5. Table (post | tree, in m)

   Height 1.5 | ?, with the arrow × 10 from the post to the tree. Both stand straight up and the sun makes the same angle for both (sketch, not to scale).

6. 3.

   Esme stands a 1.5 m post in the sun. The tree's shadow is 10 times as long as the post's shadow. How many meters tall is the tree?

   15

7. Table (stick | house, in m)

   Height 1.2 | ?, with the arrow × 5 from the stick to the house. Both stand straight up and the sun makes the same angle for both (sketch, not to scale).

8. 4.

   Jun stands a 1.2 m stick in the sun. The house's shadow is 5 times as long as the stick's shadow. How many meters tall is the house?

   6
9. 5.

   Kira draws a small triangle FQS inside a big triangle FGH. They share corner F. Which side of FGH matches side FQ?

   • side FG
   • side GH
   • side QG
10. 6.

    Luz draws a small triangle CDU inside a big triangle CVW. They share corner C. Which side of CVW matches side CU?

    • side UW
    • side CW
    • side VW
11. 7.

    Milo draws a small triangle SUV inside a big triangle SYW. They share corner S. Which side of SYW matches side UV?

    • side SY
    • side SW
    • side YW
12. 8.

    Noah draws a small triangle GQD inside a big triangle GHF. They share corner G. Which side of GHF matches side QD?

    • side GH
    • side GF
    • side HF
13. 9.

    Ren draws a small triangle CDU inside a big triangle CVW. The scale factor from the small triangle to the big one is 2. How many cm long is side CV?

    14
14. 10.

    Ari draws a small triangle WYD inside a big triangle WCV. The scale factor from the small triangle to the big one is 4. How many cm long is side WC?

    32