Missing sides of similar triangles, and shadow problems

Answer Key - Grade 8 Math Worksheet

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

1. Read this first

   Table (pole | tower, in m)

   Height 2 | ?, shadow 3 | 24. Both stand straight up and the sun makes the same angle for both (sketch, not to scale).

2. 1.

   Esme stands a 2 m pole in the sun, and its shadow is 3 m long. At the same time the tower's shadow is 24 m long. How many meters tall is the tower?

   16

3. Table (pole | house, in m)

   Height 1.2 | ?, shadow 2 | 12. Both stand straight up and the sun makes the same angle for both (sketch, not to scale).

4. 2.

   Kira stands a 1.2 m pole in the sun, and its shadow is 2 m long. At the same time the house's shadow is 12 m long. How many meters tall is the house?

   7.2

5. Table (post | house, in m)

   Height 1.6 | ?, shadow 2.5 | 10. Both stand straight up and the sun makes the same angle for both (sketch, not to scale).

6. 3.

   Luz stands a 1.6 m post in the sun, and its shadow is 2.5 m long. At the same time the house's shadow is 10 m long. How many meters tall is the house?

   6.4

7. Table (stick | school, in m)

   Height 1.8 | ?, shadow 3 | 18. Both stand straight up and the sun makes the same angle for both (sketch, not to scale).

8. 4.

   Milo stands a 1.8 m stick in the sun, and its shadow is 3 m long. At the same time the school's shadow is 18 m long. How many meters tall is the school?

   10.8
9. 5.

   Pia draws a small triangle CDU inside a big triangle CVW. How many cm long is side VW?

   17.5
10. 6.

    Ren draws a small triangle SUV inside a big triangle SYW. How many cm long is side YW?

    13.5
11. 7.

    Tala draws a small triangle GQD inside a big triangle GHF. How many cm long is side HF?

    21.6
12. 8.

    Bo measures a ramp: it rises 0.4 m over every 5 m of ground. A bigger triangle under the same ramp has a base of 25 m. How many meters high is it?

    2
13. 9.

    (sketch, not to scale). Every number is in meters. Kira measures a 2 m stick: its shadow is 3 m. At the same time the tower's shadow is 18 m. Which table sets up the problem to find the tower's height?

    • Height | Shadow: stick 2 | 3, tower 18 | ?
    • Height | Shadow: stick 2 | 3, tower ? | 18
    • Height | Shadow: stick 3 | 2, tower ? | 18

14. Use this

    The pole and the tree both stand straight up, and the sun makes the same angle for both (sketch, not to scale). Every number is in meters.

15. 10.

    Luz measures a 1.2 m pole: its shadow is 1.6 m. At the same time the tree's shadow is 20 m. Which table sets up the problem to find the tree's height?

    • Height | Shadow: pole 1.2 | 1.6, tree 20 | ?
    • Height | Shadow: pole 1.6 | 1.2, tree ? | 20
    • Height | Shadow: pole 1.2 | 1.6, tree ? | 20