##
* *Reflection: Vertical Alignment
Finding Angle Measurements Using Trig - Section 2: Solving More Problems

**Problems 7 and 8**, the word problems without diagrams, might prove difficult for some students to start. For those students, my support questions focus on reading the question and on the drawing of the diagram. I might ask the student to read the question aloud to me, one sentence or clause at a time, and then have him or her fill in the diagram accordingly, before moving on to the next phrase. I have found that struggling students often don’t even bother to read the question before giving up, so that I work on teaching them how to approach the problem, rather than just on how to do the problem. Problem 8 includes a little extraneous information that I have removed in the modified version of the problem set.

For **Problems 9 and 10**, in which no right angle is initially present in the diagram, my questions for those students who struggle focus on what must be present in order to use right triangle trig – namely a right angle. Problem 9 does not include the word *isosceles* but students should realize from the given information that it is isosceles, and will hopefully remember from earlier in the year that the altitude from the vertex angle of an isosceles triangle bisects the base; if not, this is a good opportunity to revisit triangle congruence (in this case, HL).

**Problem 10** involves a parallelogram. The students have not yet studied quadrilaterals, but the problem does not require any knowledge of a parallelogram beyond the fact that the opposite sides and angles of a parallelogram are congruent. Some students may need reassurance of these facts, but most will just assume that this is the case.

**Problem 12**, the proof of the Pythagorean identity, begins with the students examining the results when specific values for *x* are typed into their calculators. Students may need some help with entering the correct number and placement of the parentheses.

**Problem 13**, proof of the Law of Sines, requires that students draw in and label an altitude of the triangle. This skill was already included in Problems 7 and 8, so I don’t think this problem is too much of a stretch.

*Vertical Alignment: About these problems*

# Finding Angle Measurements Using Trig

Lesson 3 of 3

## Objective: Students will be able to find angle measures using trigonometry, and apply their knowledge to solving triangles. Students also derive the Law of Sines.

#### Introductory Problem

*3 min*

As the students enter the room, the Lighthouse Problem is on the board and I hand out a paper copy to the students. I ask the students to set up the problem. They are familiar with angle of elevation and depression, but their work may come to a screeching halt when it comes to actually finding the angle. After giving students a minute or two to think about it, I plan to introduce the inverse trig functions on the graphing calculator, and then allow them to finish this problem, as well as the other problems included at the end of the lighthouse problem. This type of opening often motivates my students to pay attention for the rest of the lesson. Caution: New Skills Ahead!

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#### Solving More Problems

*40 min*

To begin this segment of the lesson I hand out the Finding Angle Measures problem set. It includes 3 types of problems:

- Standard problems in which the students use trigonometry to find angles and lengths of sides of right triangles, including 2 word problems in which students must draw their own diagrams. (Problems 1-8)
- Non-standard problems in which the students are given figures without right angles. The students will need to draw in the heights of the figures in order to solve the problems using trig. (Problems 9 and 10)
- Problems in which the students focus on the definitions of the trig functions to answer the questions. These problems include proving the Pythagorean identities and the Law of Sines. For those students needing scaffolding, I have included a modified version of this assignment, which helps to lead them through the steps of the proofs. (Problems 11-13)

I also provide Answers to Finding Angle Measures that can be handed out to the students or posted somewhere in the room, so that they can check their work periodically. Students work in their groups, and I walk around the room providing support questions where needed.

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#### Lesson End

*2 min*

To bring this lesson to closure, I hand out a slip of paper (Reflection) to the students on which I ask them to reflect upon:

** How is trig going for you? Is there anything on which you are struggling? **

** What do you find easy? What do you find hard?**

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