Lesson 2: 6.2 Right Triangle Trigonometry

What are the six trigonometric ratios (sine, cosine, tangent, cosecant, secant, cotangent)?

How are these ratios defined in terms of the
sides of a right triangle?

How can we use trigonometric ratios to find missing side lengths and angle measures in a right triangle?

What is the angle of elevation/depression?

How can we use trigonometric ratios to solve problems involving angles of elevation and depression?
What are some real-world applications of angles of elevation and depression?

Trigonometric ratios, reciprocal and quotient identities, special triangles: 30°:60°:90° and 45°:45°:90°, angles of elevation and depression

HS.MA.4C - 4C. Define trigonometric ratios, solve problems involving right triangles, and apply them in real world situations

By the end of this lesson, students will be able to apply their knowledge of trigonometric ratios to solve a variety of right triangle problems, including those involving angles of elevation and depression.

Purpose: Students will apply their knowledge of trigonometric ratios (sine, cosine, tangent) to solve right triangle problems, including real-world applications involving angles of elevation and depression.

DOK Level: 2 (Understanding)

Finding the height of a tree: Measure the distance from the tree, the angle of elevation to the top of the tree, and use the tangent function to calculate the height.

Calculating the length of a shadow: Measure the height of an object, the angle of elevation of the sun, and use the tangent function to calculate the length of the shadow.

Determining the distance to an object: Measure the angle of elevation to the top of an object, the angle of depression to the bottom of the object, and the height of the object, then use trigonometric ratios to calculate the distance.

Students may confuse the ratios, especially when dealing with reciprocal functions (cosecant, secant, cotangent).

Students might not use their calculators correctly, especially when dealing with inverse trigonometric functions.

Students may struggle to correctly identify and label angles of elevation and depression in diagrams.

Students may choose the wrong trigonometric ratio to solve a problem.

Use technology tools like graphing calculators and online simulations to enhance understanding and engagement.

Encourage students to work together in small groups to discuss ideas and solve problems.

Do Now Questions

Exit Slips

Quizzes

Textbook and supplementary materials in class

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