Name _______________________ 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.
∆𝑬𝑨𝑫
∆𝑭𝑨𝑪
∆𝑮𝑨𝑩
⦟ 𝐸𝐴𝐷 =
⦟ 𝐹𝐴𝐶 =
⦟ 𝐺𝐴𝐵 =
⦟ 𝐴𝐷𝐸 =
⦟ 𝐴𝐶𝐹 =
⦟ 𝐴𝐵𝐺 =
⦟ 𝐷𝐸𝐴 =
⦟ 𝐶𝐹𝐴 =
⦟ 𝐵𝐺𝐴 =
Segment EA ≈
Segment FA ≈
Segment GA ≈
Segment AD ≈
Segment AC ≈
Segment AB ≈
Segment DE ≈
Segment CF ≈
Segment BG ≈
For each triangle, form ratios using its segment lengths, then write them in decimal form, round to four decimal
places.
∆𝑬𝑨𝑫
∆𝑭𝑨𝑪
∆𝑮𝑨𝑩
𝐸𝐴
𝐴𝐷
𝐴𝐷
𝐸𝐴
𝐸𝐴
𝐷𝐸
𝐴𝐷
𝐷𝐸
𝐷𝐸
𝐸𝐴
𝐷𝐸
𝐴𝐷
𝐹𝐴
≈
𝐴𝐶
𝐴𝐶
≈
𝐹𝐴
𝐹𝐴
≈
𝐶𝐹
𝐴𝐶
≈
𝐶𝐹
𝐶𝐹
≈
𝐹𝐴
𝐶𝐹
≈
𝐴𝐶
≈
≈
≈
≈
≈
≈
𝐺𝐴
≈
𝐴𝐵
𝐴𝐵
𝐺𝐴
𝐺𝐴
𝐵𝐺
𝐴𝐵
𝐵𝐺
𝐵𝐺
𝐺𝐴
𝐵𝐺
𝐴𝐵
≈
≈
≈
≈
≈
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 group’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 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
∆𝐺𝐴𝐵
Reference Angle
Measure in
degrees
21
∆𝐹𝐴𝐶
21
∆𝐸𝐴𝐷
21
∆𝐺𝐴𝐵
∆𝐹𝐴𝐶
∆𝐸𝐴𝐷
∆𝐺𝐴𝐵
∆𝐹𝐴𝐶
∆𝐸𝐴𝐷
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?