Trig+through+similar+triangles



Trigonometry through similar triangles



TOPIC: Trigonometry through similar triangles

GOAL: G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of angles in the triangle, leading to def of trig ratios for acute angles. 1. Have a knowledge of the concept of ratio. 2. Have the ability to convert fractions to decimal places. 3. Be able to measure the length of sides of triangles to the nearest millimeter.

LEARNING CYCLE

DEVELOP UNDERSTANDING Launch: Give the students, protractors, rulers, similar triangles, etc. that they need for the Similar triangle activity posted below Task 1: Explore: Students will work in groups to discover the ratios that similar triangles have that lead into trig ratios. Discuss: • What is the hypotenuse of a right-angled triangle? Where do you find it? • What is ratio? • What happens to the opp/hyp ratio whenthe angle is large? • What happens to the opp/hyp ratio when the angle is small?

SOLIDIFY UNDERSTANDING LAUNCH: To solidify this vast learning experience, children will engage in a discussion with the instructor about the correlation between the trig table and similar triangles. (Trig table available below) This delightful exchange will introduce an opportunity to explain the meaning and purpose of the trig keys on the calculator. Trig Tables (Thank Goodness For Calculators) EXPLORE: Students will further solidify and demonstrate their level of understanding with an engaging worksheet found (with other resources) on the worksheet link below. Task 2: DISCUSS: • What is the relationship between side ratios and the angles in a right triangle? • What is sine, cosine and tangent in relationship to the right triangle? • How do you decide which side is opposite and which is adjacent.
 * Solidify:**

PRACTICE UNDERSTANDING LAUNCH: Now that we understand the trigonometric ratios we just need to practice our understanding and we will do so by handing out a worksheet provided below. Task 3: EXPLORE: Students will complete the task with the goal of practicing the connections they have made between side ratios, angles, and trigonometric functions. DISCUSS: • Compare solutions. • Answer any remaining questions that students might have.

Extra Resources Worksheet Video Instruction

(Lack of understanding of trig functions could result in tragedy)