Grade 9-12: Geometry – Crossing the Trig River


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Content Standards

HS.G-CO.12 Make formal geometric constructions with a variety of tools and methods

HS.G-SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

HS.G-SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems

Standards for Mathematical Practice

MP 1: Make sense of problems and persevere in solving them

MP 4: Model with mathematics

MP 5: Use appropriate tools strategically


In this lesson titled “Geometry – Crossing the Trig River” by  the students use their knowledge of trigonometric relationships in order to solve a real-world problem in the context of engineering and surveying. Students use their knowledge to solve what appears to be a relatively simple question to answer. Students need to find the distance across the river only using information they can gather from their side of the river. The lesson includes objectives, different levels of assessment, and possible ways to tier the lesson and provide extensions.


Some of the cautions of this lesson include a lack of support for English language learners and does not include rubrics for assessing student progress. The lesson does not include a large amount of procedural fluency practice; it allows for students to practice in the one problem but does not extend the knowledge to other problems and applications. There is not an emphasis on technology incorporation in the lesson, one way this lesson could be improved. Connecticut teachers should note that this lesson is aligned with the high school geometry standards, despite being identified as appropriate for Grade 8 within the link.


The lesson provides a hands-on and engaging way of looking at problem-based learning. Students are provided with a contextual problem that attends to the rigor of the standards. It provides possible areas of confusion and ways to address these students. Pre-assessment, formative assessment, and post-assessment in included in the activity. Opportunities for extension and scaling are included.