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 (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).

2. 1.

   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
3. 2.

   Noah draws a small triangle FQS inside a big triangle FGH. How many cm long is side GH?

   12.5
4. 3.

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

   17.5
5. 4.

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

   13.5
6. 5.

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

   21.6
7. 6.

   Zee draws a small triangle WYD inside a big triangle WCV. How many cm long is side CV?

   7.5
8. 7.

   Ari measures a ramp: it rises 1 m over every 5 m of ground. A bigger triangle under the same ramp has a base of 20 m. How many meters high is it?

   4
9. 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
10. 9.

    Esme measures a ramp: it rises 0.6 m over every 3 m of ground. A bigger triangle under the same ramp has a base of 12 m. How many meters high is it?

    2.4

11. Use this

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

12. 10.

    Noah measures a 1.8 m stick: its shadow is 1.2 m. At the same time the house's shadow is 10 m. Which table sets up the problem to find the house's height?

    • Height | Shadow: stick 1.2 | 1.8, house ? | 10
    • Height | Shadow: stick 1.8 | 1.2, house 10 | ?
    • Height | Shadow: stick 1.8 | 1.2, house ? | 10