Do Now
 Take out your calculator
 Take a protractor from the front.
 Draw a right triangle DEF with 20o, 70o and 90o angles,
respectively. Make sure your sides are straight and your
angles are accurate.
Solving with Trig Ratios
Today’s Objectives
 Use the sine, cosine and tangent ratios to solve problems.
 Find missing sides and angles.
 Apply inverse trigonometry.
 Use problem solving skills.
Per Request
 https://www.youtube.com/watch?v=t2uPYYLH4Zo
Investigation
1.
Start with your triangle from the Do Now.
2.
Measure DE, DF, and EF to the nearest millimeter.
3.
Use your side lengths and the definitions of sine, cosine, and
tangent to complete this table. Round to four decimals.
m<D
sin D
cos D
tan D
20o
4.
sin E
cos E
tan E
70o
Share your results with your group. Calculate the average of
each ratio within your group. Create a new table with your
group’s average values.
m<D
20o
m<E
sin D
cos D
tan D
m<E
70o
sin E
cos E
tan E
Investigation
 What observations can you make about the trigonometric
ratios you found?
 What is the relationship between the values for 20o and the
values for 70o?
 Why do you think these relationships exist?
Trig Tables
Calculators of 2015
 Experiment with your calculator to determine how to find the
sine, cosine, and tangent values of angles.
 Use your calculator to compare with the trig ratios you found
by measuring sides.
Example
 Find the length of the hypotenuse of a right triangle if an
acute angle measures 20o and the leg opposite the angle
measures 410ft.
x
410 ft
20o
Example
 A right triangle has legs of length 8 inches and 15 inches. Find
the measure of the angle opposite the 8-inch leg.
8 in
xo
15 in
Practice
Practice
Practice
Today’s Objectives
 Use the sine, cosine and tangent ratios to solve problems.
 Find missing sides and angles.
 Apply inverse trigonometry.
 Use problem solving skills.
Exit Slip
1.
Find the missing side to the nearest whole cm.
b
17cm
2.
65o
Find the perimeter of this right triangle.
85m
35o
Honors Exit Slip
1.
Find the missing side to the nearest whole cm.
b
17cm
2.
65o
Find the perimeter of this rectangle.
85m
35o