Name __ANSWERS____________
Discovering Trig
A) Observe 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.
21°
21°
21°
90°
90°
90°
69°
69°
69°
19.5 cm
16.2 cm
9.5 cm
18.3 cm
15 cm
8.9 cm
7.2 cm
6 cm
3.5 cm
For each triangle, form ratios using its segment lengths, then write them in decimal form, round to four decimal
places.
1.066
1.08
1.067
.938
.926
.9368
2.708
2.7
2.71
2.542
2.50
2.54
.369
.370
.368
.393
.400
.393
C) Write a sentence describing what you notice about the angles, lengths and ratios of your data.
Answers will vary but should elude to that each to the nearest tenth that there is a relationship between sets of
3 segments in the triangle. Further explanation should also elude to that the segments are all located on
corresponding sides of the similar triangles.
D) After comparing your data with the data of your group, what do you notice about your group’s data?
Answers will vary but should elude that the class data helps to verify the individual findings and that measure
error may slightly effect the calculations, but basically there is a relationship between the ratios formed
between sides of triangle.
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.
Since there is a relationship resulting in a specific ratio between the sides and angles in a right triangle we can
use this relationship to find missing sides/angles in a right triangle.
F) Using your scientific calculator, find the 3 trigonometric ratios for each triangle’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
Reference Angle
Measure in
degrees
°
Sin
Cos
Tan
0.3584
0.9336
0.3839
21°
0.3584
0.9336
0.3839
21°
0.3584
0.9336
0.3839
69°
0.9336
0.3584
2.6051
69°
0.9336
0.3584
2.6051
69°
0.9336
0.3584
2.6051
90°
1
0
---
90°
1
0
---
90°
1
0
---
G) Compare your two charts. Describe what you notice.
Answers will vary: The ratios of certain sides give an answer very close to the sin, cos and tan that was used on
the calculator.
H) Compare your findings with your group and describe what you discover.
Answers will vary: Similar results as the individual’s
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.
J) How would your answers from your chart change if you used the other acute angle in the triangle to so this
activity?
By using a different reference angle the ratios will change, but the calculations will be similar between the
similar triangles.