Download Activity: Trigonometric Ratios and Tables Name

Activity: Trigonometric Ratios and Tables
Chapter 7-4: Trigonometry
Name: _______________________________________
Date: Feb. 18 (Sec 2) or Feb. 19 (Sec 1)
Overview: Students encounter trigonometry and discover the sine, cosine, and tangent ratios.
What's trigonometry?
INVESTIGATION #1:
Use a ruler and protractor and draw a right triangle with a 31˚ acute angle. Then measure all three sides to the
nearest millimeter and record the measurements on your drawing.
TRIGONOMETRIC RATIOS (There are 6 trigonometric ratios, but we will focus on 3 for now.)

Sine (“sin”):

Cosine (“cos”):

Tangent (“tan”):
EXAMPLE #1:
INVESTIGATION #2: TRIGONOMETRIC TABLES
In this investigation you will make a small table of trigonometric ratios for angles measuring 20˚ and 70˚.
1) Use your protractor to make a large right triangle ABC with 𝒎∠𝑨 = 20˚, 𝒎∠𝑩 = 90˚, and 𝒎∠𝑪 = 70˚.
2) Measure AB, AC, and BC to the nearest millimeter.
3) Use your side lengths and the definitions of sine, cosine, and tangent to complete the table below. Round
your calculations to the nearest thousandth.
4) Share your results with your group. Calculate the average of each ratio within your group. Create a new
row below your data and record your group’s average values.
5) Discuss your results. What observations can you make about the trigonometric ratios you found? What is
the relationship between the values for 20˚ and the values for 70˚? Explain why you think these
relationships exist.
Today, trigonometric tables have been replaced by calculators that have sin, cos, and tan keys.
6) Experiment with your calculator to determine how to find the sine, cosine, and tangent values of angles.
7) Use your calculator to find sin 20˚, cos 20˚, tan 20˚, sin 70˚, cos 70˚, and tan 70˚. Check your group’s table.
How do the trigonometric ratios found by measuring sides compare with the trigonometric ratios you
found on the calculator?
Using a table of trigonometric ratios, or using a calculator, you can find the approximate lengths of the sides of a
right triangle given the measures of any acute angle and any side.
Example #2: Find the length of the hypotenuse of a right triangle if an acute angle measures 20˚ and the side
opposite the angle measure 410 feet.
HW: Trigonometric Ratios: Show work below, or on a separate sheet of paper with your name on it (staple or place
inside A3 paper). Check selected answers on Edmodo.
For #1 and #2, find each trigonometric ratio.
1)
2)
For #3 and #4, find the measure
of each angle to the nearest ˚.
3) 𝒕𝒂𝒏 𝑪 = 𝟎. 𝟓𝟕𝟕𝟑
4) 𝒕𝒂𝒏 𝒙 =
𝟒𝟖
𝟏𝟎𝟔
For #5 through #10, find the values of the lettered measures accurate to the nearest whole unit.
5) ______________
6) __________________
7) _________________
8) _______________
9)* ___________________
10) ___________________