Handheld Trigonometry
Unit circle for trigonometry.Copyright Dave Pape http://resumbrae.com/ub/dms423_f05/10/
Students explore the concept of similar right triangles and how they apply to trigonometric ratios. Use this lesson as a refresher of what trig ratios are and how they work. In addition to trigonometry, students explore a clinometer app on an Android® or iOS® device and how it can be used to test the mathematics underpinning trigonometry. This prepares student for the associated activity, during which groups each put a clinometer through its paces to better understand trigonometry.
Some objects and distances in our world are very difficult—even impossible—to directly measure by hand or with tools. Engineers who design different types of structures, either incredibly large or very small, or machines, which might travel distances deep under the sea or far into space, must have an accurate understanding of lengths and dimensions, even when they cannot be measured. Often in these cases, engineers use trigonometry and other mathematical relationships to find very close approximations to lengths and dimensions. In the design of large structures, engineers must ensure that forces acting on the structure will balance so that they remain stationary. Engineers use trigonometry to account for vertical and horizontal components of the different forces that act on structures, thus determining that the structure will be able to stand without collapsing before it is even constructed. These strategies, based on mathematical knowledge, enable engineers to design solutions to problems that might otherwise be unsolvable.
After this lesson, students should be able to:
- Describe how a clinometer can be used by engineers.
- Use a clinometer to measure angles.