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## The Archer Fish, Geometry, and Physics

The Archer Fish earns its name because it accurately sprays jets of water at insect prey, knocks them into the water, and has a quick meal. The ability to accurately do this has to overcome several geometric and physical challenges. In this module students explore these challenges in more detail.

In fact there are three mathematical physics challenges that are explored:

• Using they Pythagorean Theorem to find the distance the Archer Fish needs to spray its jet of water
• Using the Tangent Ratios and their inverses to find the angle of the spray of water
• Taking refraction into account by using Snell's Law

#### Math Concepts

• Problem Solving
• Geometry
• Equations
• Algebra

#### Learning Objectives

• Use the Pythagorean Theorem to calculate the hypotenuse
• Calculate tangent ratios and their inverses
• Solve equations with trigonometric functions and their inverses

#### Prerequisite Skills

• Knows the basics of right triangles
• Knows the basics of ratios
• Understands what the inverse of a function is
Common Core Standards CCSS.MATH.CONTENT.HSG.SRT.C.6, CCSS.MATH.CONTENT.HSG.SRT.C.8 20 mins 9th - 11th Grade

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