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.
Name |
Description |
Similarity and Trigonometry Connections | The properties of similarity and the corresponding sides of right triangles are used to discover a pattern that leads to the three trigonometric ratios: sine, cosine, and tangent. |
Discovering Trigonometric Ratios | Students investigate and discover trigonometric ratios by drawing and measuring side lengths for five triangles that have equivalent angle measure. Students collect, analyze, and discuss data to draw conclusions. This is the introductory lesson to facilitate student discovery of trigonometric ratios and allows students to secure a solid foundation before the use of trigonometry to find missing sides. This lesson has students solving application problems by finding an unknown angle based on length measurements. |
The Copernicus' Travel | This lesson uses Inverse Trigonometric Ratios to find acute angle measures in right triangles. Students will analyze the given information and determine the best method to use when solving right triangles. The choices reviewed are Trigonometric Ratios, The Pythagorean Theorem, and Special Right Triangles. |
Geometry Problems: Circles and Triangles | This lesson unit is intended to help you assess how well students are able to use geometric properties to solve problems. In particular, the lesson will help you identify and help students who have the following difficulties solving problems by determining the lengths of the sides in right triangles and finding the measurements of shapes by decomposing complex shapes into simpler ones. The lesson unit will also help students to recognize that there may be different approaches to geometrical problems, and to understand the relative strengths and weaknesses of those approaches. |
Rockin' Right Triangle Ratios | Special Right Triangles and the ratios that work when you have to do to learn those ratios for 30-60-90 and 45-45-90 triangles. |
Calculating the Earth-Sun distance using Satellite Observations of a Venus Transit | Every school child learns that the earth-sun distance is 93 million miles. Yet, determining this distance was a formidable challenge to the best scientists and mathematicians of the 18th and 19th centuries. The purpose of this lesson is to use the 2012 Transit of Venus as an opportunity to work through the mathematics to calculate the earth-sun distance. The only tools needed are basic knowledge of geometry, algebra, and trigonometry. The lesson is self-contained in that it includes all the data needed to work through the exercise. |