Right triangles form a number of special relationships among their lengths and angle measures extending to real-world problems that often have limited information.
Focus TEKS
G.5D Identify and apply patterns from right triangles to solve meaningful problems, including special right triangles (45-45-90 and 30-60-90) and triangles whose sides are Pythagorean triples. (R)
G.11C Develop, apply, and justify triangle similarity relationships, such as right triangle ratios, trigonometric ratios, and Pythagorean triples using a variety of methods (R)
Ongoing TEKS
G.5A use numeric and geometric patterns to develop algebraic expressions representing geometric properties. (R)
G.11B Use ratios to solve problems involving similar figures (S)
Students will know…
the two special right triangles
the parts and names of the lengths of a right triangle when referenced from a given angle
the appropriate trig ratio to solve problems for missing sides or missing angles
angles of elevation and depression
Students will be able to…
derive the special right triangle formulas as a consequence of the Pythagorean Theorem
use proportions to solve special right triangles
solve real-world problems involving special right triangle
connect trig ratios to right triangles
solve real-world problems involving trigonometric ratios
find missing lengths of a right triangle using the geometric mean
determine whether a solution is reasonable
Cornell Notes
Part 1: Pages 1-5
Part 2: Pages 6-14
Classwork can be accessed at apollo.atlaslearning.net
PDF's of classwork handouts (minus warm ups) are also available below.
Classwork Part 1 - Special Right Triangles and Angles of Elevation and Depression
Classwork Part 2 - Trigonometric Ratios and Inverse Trigonometric Functions