Download 3.2.2 Connecting Slope Ratios To Specific Angles HW

The slope ratio is
1

5
=
𝑦
20
y = 4
1
5
October 29, 2015
CO: SWBAT find
missing sides and
angles for known
slope triangles.
LO: SWBAT explain
the connection
between certain
slope ratios and
their angles.
a.
b.
2
5
2
5
1
5
1
5
𝑦
= 25
=
100
𝑥
y = 10
x = 500
c.
d.
1
1
1
1
4
4
=
13
𝑎
a = 13
e.
20
50
2
=5
𝜃 = 22°
1
=1
𝜃 = 45°
f.
a. Do you agree?
180 – (79 + 90) = 11°
b. Use what you know about the slope ratio of 11° to determine the slope ratio
for 79°.
1
5
5
1
⇒
=
5
1
𝑏
7
b = 35
c. What is the relationship of 11° and 79°? What is the relationship between their
slope ratios?
11° and 79° are complementary, and their slope ratios are reciprocals.
a. For example, since you know the slope ratio for 22°, what other angle do
you know the slope ratio for? Use tracing paper to determine a slope ratio
for the complement of each slope angle you know. Use tracing paper to
help reorient the triangle if necessary.
22° & 68°, 11° & 79°, 18° & 72°, and 45° & 45°
b. Use this information to determine the value of x in the diagram at right.
90 – 68 = 22°
2
5
5
2
⇒
=
5
2
30
𝑥
x = 12
c. Write a conjecture about the relationship of the slope ratios for
complementary angles. You may want to start with, “If one angle of a right
𝑎
triangle has the slope ratio , then …”
𝑏
𝑎
𝑏
𝑏
𝑎
If one angle of a right triangle has a slope ratio , then the complementary angle has a slope ratio .
 So far you have looked at several similar slope triangles and their corresponding
slope ratios. These relationships will be very useful for determining missing side
lengths or angle measures of right triangles for the rest of this chapter.
 Before you forget this valuable information, organize information about the
triangles and ratios you have discovered so far in the table on the Lesson 3.2.2
(“Trig Table Graphic Organizer”) Resource Page. Keep it in a safe place for future
reference. Include all of the angles you have studied up to this point. An example
for 11° is filled in on the table to get you started.