Grade 8 · Geometry & measurement

Similar triangle shadows (SAT) practice

Similar triangle shadows (SAT) is a grade 8 math skill aligned to Common Core standard 8.G.A.4: understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 similar triangle shadows (sat) problems our math games drill.

CCSS 8.G.A.410 questions in the bank
Sample questions

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Question 1easy

An 88-foot-tall lamppost casts a shadow 66 feet long. At the same time, a nearby tree casts a shadow 2121 feet long. How tall is the tree, in feet?

Use similar triangles: 86=h21\dfrac{8}{6} = \dfrac{h}{21}. Cross-multiply: 6h=1686h = 168, so h=28h = 28 feet.

Question 2easy

A 33-foot fence post casts a shadow 22 feet long. At the same time, a telephone pole casts a shadow 2828 feet long. How tall is the telephone pole, in feet?

Use 32=h28\dfrac{3}{2} = \dfrac{h}{28}. Cross-multiply: 2h=842h = 84, so h=42h = 42 feet.

Question 3easy

A person who is 55 feet tall casts a shadow 33 feet long. At the same time, a water tower casts a shadow 2424 feet long. How tall is the water tower, in feet?

Set up 53=h24\dfrac{5}{3} = \dfrac{h}{24}. Cross-multiply: 3h=1203h = 120, so h=40h = 40 feet.

Question 4easy

A parking meter that is 55 feet tall casts a shadow 22 feet long. A radio antenna casts a shadow at the same time. If the antenna is 3535 feet tall, how long is its shadow, in feet?

Use 52=35s\dfrac{5}{2} = \dfrac{35}{s}. Cross-multiply: 5s=705s = 70, so s=14s = 14 feet.

Question 5easy

A 77-foot-tall basketball hoop casts a shadow 1414 feet long. At the same time, a brick chimney casts a shadow 2020 feet long. How tall is the chimney, in feet?

Set up 714=h20\dfrac{7}{14} = \dfrac{h}{20}. Cross-multiply: 14h=14014h = 140, so h=10h = 10 feet.

Question 6medium

A student who is 44 feet tall casts a shadow 55 feet long. A building casts a shadow 6565 feet long at the same time. How tall is the building, in feet?

Set up 45=h65\dfrac{4}{5} = \dfrac{h}{65}. Cross-multiply: 5h=2605h = 260, so h=52h = 52 feet.

Question 7medium

A child who is 44 feet tall casts a shadow 66 feet long. A monument casts a shadow at the same time. If the monument is 3030 feet tall, how long is its shadow, in feet?

Set up 46=30s\dfrac{4}{6} = \dfrac{30}{s}. Cross-multiply: 4s=1804s = 180, so s=45s = 45 feet.

Question 8medium

A bush that is 22 feet tall casts a shadow 55 feet long. At the same time, a cell tower casts a shadow 9090 feet long. How tall is the cell tower, in feet?

Use 25=h90\dfrac{2}{5} = \dfrac{h}{90}. Cross-multiply: 5h=1805h = 180, so h=36h = 36 feet.

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Tests that cover similar triangle shadows (sat):
SBACSATACT AspireSC READYNC EOG/EOC
More Grade 8 skills:
Scientific notationTwo-way tablesModeling linear situationsPythagorean theoremScatterplots and trend linesSlope formulaLinear coefficient interpretationsPolygon angle formulasAll Grade 8 practice →

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