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Ski Resort: Lift Lines and Snowfall Checks

Apply the Pythagorean Theorem to ski lift spans, snowfall measurements, and three-dimensional distances at a ski resort.

Grade 8MathInteractive · Printable

Aligned to8.G.B.7

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What’s included

Single worksheet
Auto-graded online
1 Common Core standard
Printable answer key
14 questions
Classroom-ready

Details

Format: Interactive · Printable
Grade: Grade 8
Subject: Math
Question types: Fill in the blank, Multiple choice, Short answer

About this worksheet

What students practice

Students find unknown legs and hypotenuses of right triangles in two-dimensional situations.
Students use connected right triangles to find distances in three-dimensional situations.
Students explain why perpendicular distances must be combined using the Pythagorean Theorem.

How to use

Have students sketch and label a right triangle for each situation before calculating. Allow calculators for the requested rounded answer, and discuss the final error analysis.

Curriculum

Common Core standard covered

8.G.B.7

Use the Pythagorean Theorem to find unknown side lengths of right triangles in real-world and math problems in 2-D and 3-D.

Preview

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Ski Resort: Lift Lines and Snowfall Checks

Use right triangles to find distances on the slopes and inside resort equipment.

Lift Spans and Measuring Tools

Use a² + b² = c², where c is the hypotenuse. Treat each lift span as a straight segment, ignoring cable sag. Show calculations on separate paper.

A ski lift span has a horizontal distance of 240 meters and a vertical rise of 70 meters. Find the length of the straight span.

Span length = m

Another straight lift span is 130 meters long. Its endpoints are 120 meters apart horizontally. How much higher is the upper endpoint?

Vertical rise = m

A maintenance support forms a right triangle. Its hypotenuse is 85 centimeters, and one leg is 36 centimeters. Which calculation gives the other leg's length?