1.A firefighter leans a 13-foot ladder against the exterior wall of a building. If the base of the ladder is placed 5 feet away from the wall, how high up the wall does the top of the ladder reach?
A11 feet
B12 feet
C14 feet
D8 feet
Working
Grade 8geometryOriginal practice
Geometry: The Pythagorean Theorem & Real-World Applications
Calculate hypotenuse lengths, missing legs, and distance on coordinate grids using a² + b² = c² with complete step-by-step solutions.
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Sheet D5767B12 · questions and answers share this ID
About this practice
Grade 8 · math · Matching answer key included · US Letter and A4
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Teaching guide, sample answers and curriculum references
Before you begin
Identify a right triangle and square and square-root numbers.
How to use this worksheet
- Model the target skill: apply the Pythagorean Theorem a² + b² = c² to determine unknown side lengths in right triangles. Use the first task as a guided example before asking for an independent response.
- Check readiness first: Identify a right triangle and square and square-root numbers.
- Discuss an incorrect response using this distinction: The hypotenuse is opposite the right angle; it is not always the side drawn horizontally or the side called x.
A common mistake to discuss
The hypotenuse is opposite the right angle; it is not always the side drawn horizontally or the side called x.
What to practice next
Check that a computed side length satisfies the original squared relationship.
Sample question and answer
A firefighter leans a 13-foot ladder against the exterior wall of a building. If the base of the ladder is placed 5 feet away from the wall, how high up the wall does the top of the ladder reach?
- A. 11 feet
- B. 12 feet
- C. 14 feet
- D. 8 feet
Answer: B. Here the hypotenuse c = 13 ft and one leg a = 5 ft. a² + b² = c² => 5² + b² = 13² => 25 + b² = 169 => b² = 144 => b = √144 = 12 feet.
Intended curriculum references: CCSS.MATH.CONTENT.8.G.B.7 · CCSS.MATH.CONTENT.8.G.B.8. These references describe learning goals; they are not endorsements.
Published 2026-10-02; updated 2026-10-02. Original MakeWorksheet practice. Automated consistency checks support publication; independent subject-specialist review is not recorded. Read our editorial policy.
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