Grade 8 · Math

8th grade Missing sides of similar triangles, and shadow problems worksheet

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Missing sides of similar triangles, and shadow problems

Grade 8 Math Worksheet

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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).
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?
Table (stick | tree, in m)
Height 1.2 | ?, shadow 1.5 | 18. Both stand straight up and the sun makes the same angle for both (sketch, not to scale).
Jun stands a 1.2 m stick in the sun, and its shadow is 1.5 m long. At the same time the tree's shadow is 18 m long. How many meters tall is the tree?
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).
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?
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).
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?
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).
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?
Noah draws a small triangle FQS inside a big triangle FGH. How many cm long is side GH?
Zee draws a small triangle WYD inside a big triangle WCV. How many cm long is side CV?
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?
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?
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.
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 1.8 | 1.2, house ? | 10
- Height | Shadow: stick 1.8 | 1.2, house 10 | ?
- Height | Shadow: stick 1.2 | 1.8, house ? | 10

8th grade Missing sides of similar triangles, and shadow problems worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Missing sides of similar triangles, and shadow problems. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can find a missing side or height from two similar triangles: shadows, a mirror on the ground, a bounce, a lamp, and a small triangle inside a big one.
I can pick the right sides to pair (the whole side of the big triangle, not the leftover piece) and set up a table with heights matched to heights and shadows to shadows.
I can say why the triangles are similar: two angles match.

Standard: 8.G.A.4 (partial), 8.EE.B.6 (partial)

Words to know

similar triangles: Same shape, maybe different size: matching angles equal, sides all grow by one number.

scale factor from small to big: How many times as long the big triangle's side is: big side ÷ small side.

shadow: The dark patch an object makes. Sun rays hit objects at the same angle at the same time.

the whole side: The full side of the big triangle, from the shared corner to the far corner.

the leftover piece: The part of that whole side that sticks out past the small triangle.

parallel: Two lines that never meet and stay the same distance apart.

bounce: A ball that hits the floor and leaves it at the same angle it came in.

Common mistakes

Used the scale factor the wrong way round: divided where the side or height needed multiplying.

Added a number where a scale factor multiplies: found the gap between two lengths and added it to the height. Try it together: if a 2 m stick has a 3 m shadow, how long is the shadow of a 4 m stick?

Put the numbers in the table the wrong way round: a shadow where a height belongs, or the reverse.

What to say

Ask: is the second triangle bigger or smaller, and should its side come out bigger or smaller?

Ask: which column is for heights and which is for shadows?

Questions parents ask

What is the most common mistake with missing sides of similar triangles, and shadow problems?

Used the scale factor the wrong way round: divided where the side or height needed multiplying.

How can I help my child with missing sides of similar triangles, and shadow problems?

Ask: is the second triangle bigger or smaller, and should its side come out bigger or smaller?

Are these 8th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More grade 8 math

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8th grade Missing sides of similar triangles, and shadow problems worksheet

Table (pole | tower, in m)

Table (stick | tree, in m)

Table (pole | house, in m)

Table (post | house, in m)

Table (stick | school, in m)

Use this