Using Geometry to Determine the Cost and Length of Water Slides

The video tutorial teaches how to model a word problem using trigonometric ratios and the Pythagorean theorem. It focuses on designing a water slide with specific constraints, such as ladder height and slide angle. The tutorial calculates the costs of building both the longest and shortest slides, considering different pricing for slide lengths. It concludes with a decision-making process on which slide to build, weighing cost against potential customer attraction.

What is the primary goal of mathematical modeling in the context of this lesson?

• To memorize mathematical formulas

• To analyze and solve real-world problems

• To avoid using any mathematical tools

• To create complex mathematical equations

What is the length of the longest slide when the ladder is 35 feet tall?

• 40 feet

• 30 feet

• 45.7 feet

• 50 feet

How much does it cost per foot to build a slide longer than 30 feet?

• $100

• $90

• $70

• $50

What is the length of the shortest slide when the ladder is 20 feet tall?

• 20 feet

• 26.1 feet

• 30 feet

• 35 feet

How much does it cost per foot to build a slide shorter than 30 feet?

• $50

• $70

• $90

• $100

Which slide is cheaper to build, and by how much?

• Longer slide by $1,090

• Shorter slide by $1,090

• Longer slide by $2,000

• Shorter slide by $2,000

What factors might influence the decision to build a longer slide despite its higher cost?

• The color of the slide

• The potential to attract more customers

• The availability of materials

• The length of the queue