Exploring Trigonometry Word Problems

Objective:

Students will be able to apply trigonometric ratios to solve word problems involving angles of depression and elevation.

Assessment:

Students will be assessed through a worksheet containing various trigonometry word problems that involve angles of depression and elevation. They will need to apply trigonometric ratios to calculate missing lengths.

Key Points:

• Understanding angles of depression and elevation

• Applying trigonometric ratios (sine, cosine, tangent) in word problems

• Solving for unknown lengths using trigonometry

• Interpreting the solutions in the context of the problem

Opening:

• Begin by showing students a picture with a building and asking them how they can calculate the height of the building without actually measuring it.

Introduction to New Material:

• Define angles of depression and elevation

• Explain the concept of trigonometric ratios

• Common Misconception: Assuming the angle given in the problem is always the angle needed for calculation, emphasize the need to identify the correct angle.

Guided Practice:

• Provide examples of word problems on the board

• Start with guided questions leading students through the solution process

• Monitor student understanding by walking around the classroom and checking on their progress

Independent Practice:

• Distribute a worksheet with various trigonometry word problems

• Instruct students to work independently to solve the problems

• Encourage them to show their work and explain their reasoning

Closing:

• Have students share their solutions to one of the word problems on the board

• Summarize the key steps in solving trigonometry word problems

Extension Activity:

• For early finishers, provide a challenge problem involving multiple steps and angles

Homework:

• Assign students to create their own trigonometry word problem that involves angles of depression and elevation for their peers to solve.

Standards Addressed:

• CCSS.MATH.CONTENT.HSG.SRT.D.10: Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles.

• CCSS.MATH.CONTENT.HSG.SRT.D.10a: Verify experimentally the properties of dilations given by a center and a scale factor.