Goals: Each student will use trigonometric ratios to solve for side lengths and angle measures in right triangles.
Objectives:
State Standards: MA.912.T.2.1 Define and use the trigonometric ratios in terms of angles of right triangles.
Motivation: Most students need something to draw their interest. Having already solved right triangle using the Pythagorean Theorem, I will ask students “How can we solve for a side length of a right triangle if we don’t have two other lengths? What can we do when only one side is known and an angle measure is given?” One thing I have found to engage students is to show them how to use sin, cos, and tan on their calculators because most of them have wanted to know what those buttons mean, but have not learned yet. I like to relate it back to the special right triangles and how we know the ratios of those sides for those particular angles. Using the calculator is what gives us the ratios for all right triangles.
Lesson Procedure:
1) Students must recall the properties of a right triangle (legs, hypotenuse, angles) and the Pythagorean theorem.
2) Define opposite and adjacent. Ask students to name who is on the opposite side of the room from them; ask who is adjacent to them. Show them how sides are opposite and adjacent to the acute angles of a right triangle.
3) Teach students the trigonometric ratios using the mnemonic SOHCAHTOA
Sin = Opp Cos = Adj Tan = Opp
Hyp Hyp Adj
4) First exercise, have students identify trigonometric ratios of angles in right triangles.
5) Second exercise, have students set up equations to solve for side lengths and angle measures in right triangles.
6) Third exercise, give students one ratio of a right triangle and have them determine the other ratios.
Closure: This lesson should take 1-2 class periods. Worksheet will be given for practice. Quiz will be given after lesson is finished.
Extension/Elaboration: Ask students to think of where they might find right triangles in real life. Have them discuss in groups of 3-4 how trigonometry might be applicable in these situations. Allow them to share their thoughts with the entire class.
Evaluation/Assessment: Students will take quiz over the types of problems covered in this lesson. Students will also be asked to draw a concept map listing the ideas covered throughout the lesson.
Objectives:
- Given a right triangle, the student will be able to accurately solve for one side length when given another side length and angle measure by using one of the trigonometric ratios.
- Given one trigonometric ratio related to a right triangle, the student will be able to determine the exact values of the other trigonometric ratios.
State Standards: MA.912.T.2.1 Define and use the trigonometric ratios in terms of angles of right triangles.
Motivation: Most students need something to draw their interest. Having already solved right triangle using the Pythagorean Theorem, I will ask students “How can we solve for a side length of a right triangle if we don’t have two other lengths? What can we do when only one side is known and an angle measure is given?” One thing I have found to engage students is to show them how to use sin, cos, and tan on their calculators because most of them have wanted to know what those buttons mean, but have not learned yet. I like to relate it back to the special right triangles and how we know the ratios of those sides for those particular angles. Using the calculator is what gives us the ratios for all right triangles.
Lesson Procedure:
1) Students must recall the properties of a right triangle (legs, hypotenuse, angles) and the Pythagorean theorem.
2) Define opposite and adjacent. Ask students to name who is on the opposite side of the room from them; ask who is adjacent to them. Show them how sides are opposite and adjacent to the acute angles of a right triangle.
3) Teach students the trigonometric ratios using the mnemonic SOHCAHTOA
Sin = Opp Cos = Adj Tan = Opp
Hyp Hyp Adj
4) First exercise, have students identify trigonometric ratios of angles in right triangles.
5) Second exercise, have students set up equations to solve for side lengths and angle measures in right triangles.
6) Third exercise, give students one ratio of a right triangle and have them determine the other ratios.
Closure: This lesson should take 1-2 class periods. Worksheet will be given for practice. Quiz will be given after lesson is finished.
Extension/Elaboration: Ask students to think of where they might find right triangles in real life. Have them discuss in groups of 3-4 how trigonometry might be applicable in these situations. Allow them to share their thoughts with the entire class.
Evaluation/Assessment: Students will take quiz over the types of problems covered in this lesson. Students will also be asked to draw a concept map listing the ideas covered throughout the lesson.
If you need to review the Pythagorean Theorem, click on the button below to practice.
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Click below to take quiz after lesson is taught to see how well you have learned trigonometric ratios.
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