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
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Finding Angle Measurements Using Trig

Unit 7: Right Triangle Trigonometry
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.

Big Idea: Students put their knowledge of trig to work solving problems and proving hypotheses involving angles.

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