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discovering trig

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Name _______________________ Discovering Trig
A) Observe โˆ† GBA below and label the hypotenuse, opposite side and adjacent side with respect to the
reference angle A.
B) Calculate the missing angle measures of each triangle and complete the chart. Use a ruler, and measure to
the nearest tenth of a centimeter, all three sides of the right triangles. Use the chart below to record your data
for each triangle.
โˆ†๐‘ฌ๐‘จ๐‘ซ
โˆ†๐‘ญ๐‘จ๐‘ช
โˆ†๐‘ฎ๐‘จ๐‘ฉ
โฆŸ ๐ธ๐ด๐ท =
โฆŸ ๐น๐ด๐ถ =
โฆŸ ๐บ๐ด๐ต =
โฆŸ ๐ด๐ท๐ธ =
โฆŸ ๐ด๐ถ๐น =
โฆŸ ๐ด๐ต๐บ =
โฆŸ ๐ท๐ธ๐ด =
โฆŸ ๐ถ๐น๐ด =
โฆŸ ๐ต๐บ๐ด =
Segment EA โ‰ˆ
Segment FA โ‰ˆ
Segment GA โ‰ˆ
Segment AD โ‰ˆ
Segment AC โ‰ˆ
Segment AB โ‰ˆ
Segment DE โ‰ˆ
Segment CF โ‰ˆ
Segment BG โ‰ˆ
For each triangle, form ratios using its segment lengths, then write them in decimal form, round to four decimal
places.
โˆ†๐‘ฌ๐‘จ๐‘ซ
โˆ†๐‘ญ๐‘จ๐‘ช
โˆ†๐‘ฎ๐‘จ๐‘ฉ
๐ธ๐ด
๐ด๐ท
๐ด๐ท
๐ธ๐ด
๐ธ๐ด
๐ท๐ธ
๐ด๐ท
๐ท๐ธ
๐ท๐ธ
๐ธ๐ด
๐ท๐ธ
๐ด๐ท
๐น๐ด
โ‰ˆ
๐ด๐ถ
๐ด๐ถ
โ‰ˆ
๐น๐ด
๐น๐ด
โ‰ˆ
๐ถ๐น
๐ด๐ถ
โ‰ˆ
๐ถ๐น
๐ถ๐น
โ‰ˆ
๐น๐ด
๐ถ๐น
โ‰ˆ
๐ด๐ถ
โ‰ˆ
โ‰ˆ
โ‰ˆ
โ‰ˆ
โ‰ˆ
โ‰ˆ
๐บ๐ด
โ‰ˆ
๐ด๐ต
๐ด๐ต
๐บ๐ด
๐บ๐ด
๐ต๐บ
๐ด๐ต
๐ต๐บ
๐ต๐บ
๐บ๐ด
๐ต๐บ
๐ด๐ต
โ‰ˆ
โ‰ˆ
โ‰ˆ
โ‰ˆ
โ‰ˆ
C) Write a sentence describing what you notice about the angles, lengths and ratios of your data.
D) After comparing your data with the data of your group, what do you notice about your groupโ€™s data?
E) On a half sheet of paper, write a hypothesis about the relationships among the length of the sides of the
right triangles based on the information that your group gathered and discussed. Get ready to do the Commit
and Toss activity.
F) Using your scientific calculator, find the 3 trigonometric ratios for each triangleโ€™s 3 angles. Write your
answer in the appropriate box. (The key strokes/order of entry may be different on different types of
calculators. Make sure you are in degree mode).
Triangle Name
โˆ†๐บ๐ด๐ต
Reference Angle
Measure in
degrees
21
โˆ†๐น๐ด๐ถ
21
โˆ†๐ธ๐ด๐ท
21
โˆ†๐บ๐ด๐ต
โˆ†๐น๐ด๐ถ
โˆ†๐ธ๐ด๐ท
โˆ†๐บ๐ด๐ต
โˆ†๐น๐ด๐ถ
โˆ†๐ธ๐ด๐ท
Sin
Cos
Tan
G) Compare your two charts. Describe what you notice.
H) Compare your findings with your group and describe what you discover.
I) Based on this activity write 3 general equations that can be used to show the ratio relationships of each of
the trimetric functions. Use the words hypotenuse, adjacent and opposite in your equations.
sin =
cos =
tan =
J) How would your answers from your chart change if you used the other acute angle in the triangle to so this
activity?
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