Download File

4-69. Marta arrives for her math test only to find that she has
forgotten her calculator. She decides to complete as much of
each problem as possible.
a.
In the first problem on the test, Marta has to solve for the
length x in the triangle shown at right. Using her algebra skills, she
writes and solves an equation. Her work is shown below. Explain
what she did in each step.
29
sin 25° =
𝑥
x(sin 25°) = 29
29
x=
sin 25
b.
<- Write down!
Marta’s answer in part (a) is called an exact answer. Now use your
calculator to help Marta determine the approximate value of x.
68.62
c.
Marta’s teammate, Ziv, said he solved it differently but still got the
29
same answer. He started with the equation cos 65°= . Explain
𝑥
why this equation must give the same answer.
Because 65 and 25 are complementary angles, but the 29 becomes the
adjacent with 65 degrees.
4-69.
d.
Solve for y in the diagram at right in two ways, using both sine and cosine
ratios. Make sure both strategies result in the same answer.
𝑦
5
sin 53° =
5(sin 53°) = y
y = 3.99
𝑦
cos 37° =
5
5(cos 37°) = y
y = 3.99
4.2.2 SELECTING A
TRIG TOOL
November 30, 2015
Objectives
• CO: SWBAT solve for missing sides using
sine, cosine, or tangent.
• LO: SWBAT verbally develop strategies in
their teams to recognize which
trigonometric ratio to use based on the
relative position of the reference angle and
the given sides involved.
Progress Chart
a-c
Purple
Stripes
Blue
Green
Pink
Orange
Yellow
Red
d-f
g-i
Team Roles
• Resource Manager: Pull ideas from the team. Ask questions
such as, “Does anyone have an idea?” and “Which side is
opposite the angle?”.
• Task Manager: Listen for statements and reasons. Ask
questions such as, “Why did you choose that ratio?” and “How
did you know that side is opposite?”.
• Facilitator: Keep the team together and keep the discussion
going. Ask questions such as, “Did everyone agree with her
statement?” and “Is everyone ready to move on to the next
question?”.
• Recorder/Reporter: Create large sketches of diagrams that
can be seen clearly by all team members. Ask questions such
as, “What strategies can we share with the class?”.
“Choosing a Trig Tool”
a.
b.
c.
d.
e.
f.
g.
h.
i.
Sine -> x ≈ 8.92
x = 8 (slope ratio is 1)
Cosine x ≈ 37.13
Sine -> x ≈ 14.20
x = 16 using similarity
ratio from problem 4-57
Sine
->
x = 21
x = 0 (angle collapses)
Cosine
-> x ≈ 0.88
Tangent -> x ≈ 10.80
4-70. In problem 4-68, you used trigonometric tools to solve for a side length. But do you
have a way to determine an angle measure? Examine the triangles below. Do any of
them look familiar? How can you use information about the side lengths to help you
figure out the reference angle (θ)? Your Trig Table Graphic Organizer from Chapter 3
may be useful.
9
tan𝜃=
9
𝜃 = 45°
1
tan𝜃=
5
𝜃 = 11°
1
cos𝜃=
2
𝜃 = 60°